Physics M.C.Q (1 Marks)

Potentiometer is preferred over voltmeter because it measures true emf of the cell. It uses null method so that no current is drawn from cell in balanced condition, as $E - Ir = V$ and $I = 0$ then $V = E.$
Hence emf measurement is more accurate.

$\text{P}=\frac{\text{V}^2}{\text{R}}$
As the resistors on connected in paralled to battorty, both have same patential,
$\text{p}=\frac{1}{\text{R}}$
$\frac{\text{P}_1}{\text{P}_2}=\frac{\text{R}_2}{\text{R}_1}$
$=\frac{6}{4}$
$=\frac{3}{2}$
$3:2$

The resistance of a conductor is directly proportional to its length, inversely proportional to the area of cross$-$section, and nature of the material. The resistance of the conductor does not depend on viscosity.

Power $=\frac{\text{V}^2}{\text{R}},\text{R}\downarrow\text{thanpower}\uparrow$
Because Power $\propto\frac{1}{\text{R}}.$

Equivalent emf $\in_0=\frac{\in_1\text{r}_1+\in_2\text{r}_2}{\text{r}_1+\text{r}_2}$

Equivalent resistance $=\text{r}_0=\frac{\text{r}_1\text{r}_2}{\text{r}_1+\text{r}_2}$
$\phi$ The equivalent emf is smaller than either of the two emfs.
$\phi$ The equivalent internal resistance is smaller than either of the two internal resistances.

When we measure the emf of a cell by the potentiometer then no current flows in the circuit in zero$-$deflection condition ie, cell is in open circuit. Thus, in this condition the actual value of a cell is found. In this way, potentiometer is equivalent to an ideal voltmeter of infinite resistance.
Note. The emf in the potentiometer is measured by null method in which zero deflection position is found on the wire.

Current is uniform throughout the wire even if it is of non$-$uniform thickness. This is because charge passing through every cross sectional area per unit time remains the same throughout the wire. So, current remains the same.

$‘X\ ’$ is a metallic conductor. For small currents, it obeys Ohms’s law and its $V-I$ graph is a straight line. But when large currents are passed through the same conductor, it gets heated up and its resistance increases. It no longer obeys Ohm’s law at higher currents.

Thermistor are made up of substance with high $\alpha ,$ which is very much sensitive to temperature thereby a slight change in temperature varies its resistance with huge amount. hence making more than one value of current possible for chosen non$-$zero value of voltage.

For a balanced Meter Bridge $\frac{\text{P}}{\text{Q}}=\frac{\text{x}}{(100-\text{x})}.$ From this, we can understand that the null deflection of galvanometer does not depend on the radius of the wire. So, even if the radius of the wire is tripled, the null deflection of the galvanometer undergoes no change.

Given: $P = 25W$
$V = 220$ volts
$\therefore$ Current through the lamp $\text{I}=\frac{\text{P}}{\text{V}}=\frac{25}{220}=0.114\text{A}$

Red color band in the color coding of a resistor has the tolerance of $\pm2\%$

Resistance of conductor $\text{RT}​=\text{R}\text{o}​(1+αΔ\text{T})$ where $α > 0$
Thus resistance of the conductor increases with increase in temperature.

When the battery is discharging, the terminals voltage of the battery is always $≤$ Emf of cell $[∵\text{r}>0]$
$\therefore$ There will always be a difference which is defined to be lost volt.

In wired resistors are mainly produced with alloys, since pure metal has a high temperature co$-$efficient.
Due to alloy temperature co$-$efficient of wire wound resistor is very low.
Therefore it is very less effected by temperature change.

Kirchoff's second law:- According to the law, at a particular junction the charge entering the junction is equal to charge exiting that junction.
$\Rightarrow $ There is no charge accumulated at junction. This is also called as law of conservation of charge.

$\text{EMF}$ of cell can be defined as:
$\rightarrow $ Workdone in taking unit positive charge once round the circuit.
$\rightarrow $ The open circuit voltage of cell.
$\rightarrow $ The terminal voltage when current is zero.

Specific resistance $($ or resistivity $)$ is an intrinsic property of a material i.e. it depends only on the nature of material but not on the dimensions of the conductor. Thus specific resistance remains the same even if the length of the conductor is doubled and its radius is halved.

Thermal Energy developed $=1^2 Rt ($Because in series, current is same$)$

$\frac{\text{Thermal Energy developedin "R"}}{\text{Thermal Energy developedin "2R"}}=\frac{\text{I}^2\text{Rt}}{\text{I}^2(2\text{R})\text{t}}=\frac{1}{2}$

A non$-$ohmic resistance is a resistance that does not obey $ohm’s$ law. Among the given options, a diode is a non$-$ohmic resistance.

Carbon resistor is difficult to make of having a value less than about $20 \ Ohms$ because they have ability to withstand high energy pulses, when current flow through the carbon composition body conducts the energy. So carbon resistor can be made with a higher resistance.

The rate at which energy is drawn from a source of energy when unit current flows through the circuit or device is called $e.m.f.$ It is measured in volts.

Conductivity $\sigma=\frac{1}{\rho }$ Where r is resistivily.
Product of conductity and resistivity $= 1.$

$Þ$ There is no current through $B.$
$Þ$ There is a current through $A$ as long as the charging is not complete.

The electric power line enters our house through three wires$-$ namely the live wire, the neutral wire and the earth wire. To avoid confusion we follow a colour code for insulating these wires. The red wire is the live wire, and the black wire is neutral. The earth wire is given green plastic insulation. The colour coding of wires is green for earth red for live and black for neutral.

The charge $($Positive$)$ inside the bottery my go from the positive terminal to the negative terminal.

The current that flows from a point at the lower $($negative$)$ potential to a point at higher $($positive$)$ potential is called electronic current. Electronic current is produced by the movement of negatively charged electrons.

By increasing resistance in the primary circuit the $P.G$ of the wire decreases thereby it requires more length to measure the emf of secondary cell.
By increasing the resistance in series circuit we can move balancing point from sixth to eight wire.

Electromotive Force $\text{(EMF)}$ may be defined as work done per coulomb on the charge.

The practical unit of power is horse power $(hp)$. Kilo watt is also another practical unit of power. $1$ kilowatt $= 1000$ watt; $1 hp = 746$ watt. It is usually used in reference to the output of engines or motors.

The conductors which obey $Ohm’s$ law are called Ohmic conductors. The linear relationship between voltage and current for these conductors hold good. The resistance $(\text{R}=\frac{\text{V}}{\text{I}})$is independent of the current through the conductor. The magnitude of current changes linearly with voltage. Hence the $V-I$ graph for ohmic conductors is a straight line passing through the origin.

A wire wound resistor is an electrical passive component that limits current. The resistive element exists out of an insulated metallic wire that is winded around a core of non$-$conductive material. The wire material has a high resistivity, and is usually made of an alloy such as Nickel$-$chromium $($Nichrome$)$ or a copper$-$nickel$-$manganese alloy called Manganin. Common core materials include ceramic, plastic and glass. It has a lower order of stability and reliability is not true for wire wound resistor.

p-n junction diode consists of $p-$type and $n-$type semiconductors. The $V-I$ relationship is non-linear. When a voltage is applied across junction, very little current flows for the fairly high negative voltage and a current begins to flow for much smaller positive $($forward$)$ bias. The magnitude of variation depends upon the sign of potential difference applied across it.

The equation $\rightarrow ∑e = ∑IR$ is applicable to Kirchhoff’s second law. This law is also known as Kirchhoff’s loop rule. This expression tells us that in a closed loop, the algebraic sum of the emfs is equal to the algebraic sum of the products of the resistance and currents flowing through them.

The current that flows from a point at the higher $($positive$)$ potential to a point at lower $($negative$)$ potential is called conventional current. The direction of motion of positive charges is taken as the direction of electric current.

$\text{E.m.f}$ of a cell is defined as the maximum potential difference across the cell when no current flows through the circuit.

Wheatstone bridge is an arrangement of four resistors $\text{P, Q, R,}$ and $S$, such that if we know the value of the resistances of any three of them, we can obtain the value of fourth unknown resistance. Therefore, there are $4$ resistances in a Wheatstone bridge.

Kirchhoff’s $2^{nd}$ year is applied in a closed loop. Kirchhoff’s $2^{nd}$ law supports the law of conservation of energy. This means that energy is neither created nor destroyed in the closed loop. Whatever energy enters the loop, same amount leaves the loop.

Key concept: In this problem, the concept of balanced Wheatstone bridge is to be used.
Condition of balanced wheat stone bridge: The bridge is said to be balanced if the ratio of the resistances in same branch is equal $\frac{R}{S}=\frac{I_1}{\left(100-I_1\right)}$.
Wheatstone bridge is an arrangement of four resistances which can be used to measure one unknown resistance of them in terms of rest.
The percentage error in $R$ can be minimised by adjusting the balance point near the middle of the bridge, i.e., when is close to $50 \ cm $. This requires a suitable choice of $S$.
Since, $\frac{R}{S}=\frac{I_1}{\left(100-I_1\right)}$
Since here, $R: S=2.9: 97.1$
Then the value of $S$ is nearly $33$ times to that of $R$. In order to make this ratio $1: 1$, it is necessary to reduce the value of $S$ nearly $\frac{1}{33}$ times, i.e., nearly $3 \Omega$.

emf of secondary cell $= I r l$
where
$I -$ current in the main circuit from battery.
$r -$ resistance per unit length of wire.
$l -$ balancing length.

$\phi$ Kirchhoff's Junction Law follows from conservation of charge.
$\phi$ Kirchhoff's loop law fallows from conservation nature of electric field.

Most of the metals obey Ohm’s law and they are called ohmic conductors. Whereas semiconductors are non$-$ohmic. Nichrome metal is an ohmic conductor in which the $V-I$ characteristic has a straight line passing through the origin.

If we add two non ideal batteries in series then.
so in case $(a)$ the equivalent $e.m.f.$ may be larger than either of two $e.m.f.$, but in case $(b)$ the equivalent $e.m.f.$ may be smaller than either of two $e.m.f.$
In series total resistance is always greater than individual resistance, whether batteries are connected in any way
[i.e. either according to case $(a)$ or case $(b)].$

The drift velocity of electrons decreases when the length of the conductor is increased.
Drift velocity $=\frac{\text{Potentialdifference}}{\text{(numberofelectrons×chargeofelectron×lengthofconductor×density).}}$

Current $I_4$ can be calculated using Kirchhoff’s first law. The sum of current arriving at a junction is equal to the currents leaving the junction.
Here, Currents arriving at a junction: $7A + 5A = 12A$
Currents leaving the junction: $3A + I_4$
Equating both the currents: $12A = 3A +I_4$
$I_4 = 9A$

The resistivities of semiconductors lie between $10^{-6} \Omega m$ and $10^4 \Omega m$.. A semiconductor material has an electrical conductivity value falling between that of a conductor, such as metallic aluminum, and an insulator, such as wood. Silicon and germanium are typical semiconductors.

Potentiometer is an electric instrument used to measure internal resistance, electromotive force $(emf)$, and it is also used for comparing the emfs of different cells. Potentiometer can be used as a variable resistor as well.

Silicon is an example of a non$-$ohmic conductor. It exhibits non$-$linear behaviour. After a certain voltage, the current decreases as the voltage increases. The $V-I$ plot for silicon is non-linear.

Temperature of a cunductor increases that causes resistivity $(r)$ is increases due conductivity $(s)$ is decrease.
$\therefore\sigma=\frac{1}{\rho}$
$\Rightarrow\text{ratio of}\frac{\text{resistivity}}{\text{conductivity}}=\frac{\rho}{\sigma}=\rho^2$ is increase.

According to $Ohm's$ law, the potential difference across a conductor is directly proportional to the current through it.
$V = IR$
Hence the curve is a straight line passing through origin.

Electrolysis of an aqueous solution of table salt $(\text{NaCl}$, or sodium chloride$)$ produces aqueous sodium hydroxide and chlorine, although usually only in minute amounts. $\text{NaCl} ($aq$)$ can be reliably electrolysed to produce hydrogen. Hydrogen gas will be seen to bubble up at the cathode, and chlorine gas will bubble at the anode.
As the electricity from the battery passes through and between the electrodes, the water splits into hydrogen and chlorine gas, which collect as very tiny bubbles around the electrode tips. Hydrogen collects around the cathode and chlorine gas collects around the anode.

Number of cells $(n)=36$; Emf of each cell $(e)=4 V$; Total emf $(E)=88 V$;
Let the number of reversed cells be ' $y$ '
The required equation: $E_{E F F}= n \times e -2 y \times e$
$88=36 \times 4-2 y \times 4$
$88=144-8 y$
$8 y=56$
$y=7$

$\text{Q}=\text{CE}\Big(1-\text{e}^{\frac{-\text{t}}{\text{Rc}}}\Big)$
$\text{C}-500\times10^{-6}\text{F}$
$\text{R}=10^4\text{W}$
$\text{t}=\text{Rc}=10^4\times500\times10^{-6}=5$
$\text{t}=5\text{sec}$
$\text{Q}=\text{C}\in\Big(1-\text{e}^{-\text{t}}\Big)=\text{C}\in\Big(1-\frac{1}{\text{e}}\Big)=0.63\text{c}\in$
Thus, $63\%$ of the maximum charge is deposited in one time constant.

With the help of the figure we can say that the capacitor in the first $5s$ is larger than the charge stored in the next any second.
$\Rightarrow\text{at}\ \text{t}=\infty$
$\text{Q}=\text{Q}_0\Big(1-\text{e}^{-\infty}\Big)=\text{Q}_0=\text{C}\in$
$\therefore\text{t}_\infty-\text{t}_5=\text{C}\in-63=37$
after $t = 5 \sec$., maximum charge is deposited is only $37\%.$

Key concept: Current per unit area $($taken normal to the current$), \frac{\text{I}}{\text{A}}$, is called current density and is denoted by $\vec{\text{J}}$.

The is unti of the currnt density are $\frac{\text{A}}{\text{m}^2}$. The current density is also directed along $E$ and which is also a vector quantity and the relationship is given by
$\vec{\text{J}}=\sigma\vec{\text{E}}=\frac{\vec{\text{E}}}{\rho}$
where $\sigma$ = conductivity and $\rho =$ resistivity of specific resistance of the the surface of wire.

An electrochemical cell is a device which converts chemical energy to electric energy, and maintains the flow of charge in a circuit. There are $2$ types of electrochemical cells $–$ Galvanic cell and Electrolytic cell.

As, $\text{R}=\rho\Big(\frac{\text{I}}{\text{A}}\Big)$
If we calculate $R$ with the help of above relation then,
From option $(a)$ we will get $\text{R}=20\rho\Omega$
From option $(b)$ we will get $\text{R}=\Big(\frac{\rho}{20}\Big)\Omega$
From option $(c)$ we will get $\text{R}=\Big(\frac{\rho}{5}\Big)\Omega$
Clearly, the resistance will be maximum when the battery is connected across $1\text{cm}\times\frac{1}{2}\text{cm}$ faces.

Tolerance level of
Green: $0.5\%$
Blue: $0.25\%$
Violet: $0.1\%$

When n identical cells, each of emf $' e\ '$ and internal resistance $' r\ '$ are connected to the external resistance $' R\ '$ in series, its called series grouping. In series grouping $e _{ eq }= ne$ and $r _{ eq }= nr$ Therefore, current in the circuit $( l )=\frac{ ne }{( R + nr )}$

A wire bound resistor is an electrical passive component that limits current. Wire$-$bound resistors are made by winding the wires of an alloy like manganin on an insulating base. They are relatively insensitive to temperature.

$\text{R}=\frac{\rho}{\text{A}}=50$


resistance of $'5\ '$ equal parts are same.
$\text{R}'=\frac{\frac{\rho}{5}}{\text{A}}=\frac{50}{5}=10\Omega$
All '5' equal parts connect in parallel,

$\frac{1}{\text{R}_\text{eq}}=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}=\frac{5}{10}$
$\text{R}_\text{eq}=2\Omega$

Thermal Energy developed $=\frac{\text{v}_2}{\text{R}}\text{t} ($Because in Parallel, voltage is same$)$

$\frac{\text{Thermal Energy developedin "R"}}{\text{Thermal Energy developedin "2R"}}=\frac{\frac{\text{v}^2}{\text{R}}\text{t}}{\frac{\text{v}^2}{2\text{R}}\text{t}}=2:1$

The $V-I$ graph gives the characteristic of a semiconductor. It exhibits non$-$linear behaviour. After a certain voltage, the current decreases as the voltage increases. Gallium arsenide shows this type of behaviour.

Conductors have low resistivities in the range of $10^{-8} \Omega m$ to $10^{-6} \Omega m$.. Metals are good conductors. Conductors are objects or types of material that allows the flow of charge in one or more directions, and a result, the resistance offered against the flow of charge will be less.

Watt is the $SI$ unit of power.
$\text{Power}=\frac{\text{Work done}}{\text{time}}$.
The $SI$ unit of work done is the same as energy, that is, joule and that of time is seconds. Therefore, one watt is equal to one joule per second.

vd drift velocity $=\frac{1}{2}\Big(\frac{\text{eE}}{\text{m}}\Big)\text{t}$
$\text{K.E}.=\frac{1}{2}\text{mv}^2_\text{d}=\frac{1}{2}\text{m}\Big(\frac{1}{4}\frac{\text{e}^2\text{E}^2\text{t}^2}{\text{m}^2}\Big)$
$\text{K.E}.=\frac{1}{8}\frac{\text{e}^2\text{E}^2\text{t}^2}{\text{m}}$
$\text{p}=\text{K.E}.\propto\frac{1}{\text{m}}$
Mass of electron $<$ mass of metalions.
$K.E.$ of electron $> K.E.$ of metalions.

The quantity of charge passing through any cross$-$section per second is nothing but current flowing in the conductor.
As given, the current is steady current, means current is uniform throughout the cross$-$section. Hence it is independent of Area of cross section.

The rate of flow of electric charge through any cross$-$section of a conductor is known as electric current.

Components connected in series are connected along a single path, so the same current flows through all of the components. The current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component. In a series circuit, every device must function for the circuit to be complete. One bulb burning out in a series circuit breaks the circuit. A circuit composed solely of components connected in series is known as a series circuit.
The total resistance of resistors in series is equal to the sum of their individual resistances. Hence, the Equivalent resistance is more than the individual resistances because a sum is taken of all the individual resistances. That is, $R_{\text {total }}=R_1+R_2$. The current is given as $I=I_1=I_2$.
Below is the diagrammatic representation of $2$ resistors $R_1$ and $R_2$ connected in series.