[2 Mark Question Answer]

Question 12 Marks

A cell of e.m.f. $E =2 V$ and internal resistance $r=1 \Omega$ is connected to an external resistance $R=4 \Omega$ as shown in the figure. The voltmeter $V$ measures the terminal voltage across the cell while the ammeter A measures the current in the circuit.

Complete the table, using the labels from the figure. The first label is done for you.

Answer

(b) 2 V
(c) $0.4 A\left[\because I =\frac{ E }{ R +r}-\frac{2 V}{(4+1) \Omega}=\frac{2 V}{5 \Omega}=0.4 A\right]$
(d) $1.6 V .[\because V = E - Ir =2 V-0.4 A \times 1 \Omega=2 V-0.4 V=1.6 V]$
(e) $r=\frac{( E - V )}{ I }$

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Question 22 Marks

A cell of emf 2 V and internal resistance $1.2 \Omega$ is connected with an ammeter of resistance $0.8 \Omega$ and two resistors of $4.5 \Omega$ and $9 \Omega$ as shown in the diagram :
(a) What would be the reading on the Ammeter?
(b) What is the potential difference across the terminals of the cell?

Answer

Resistance of $4.5 \Omega$ and $9 \Omega$ in parallel
$\frac{1}{R_p}=\frac{1}{4.5}+\frac{1}{9}=\frac{2+1}{9}=\frac{1}{3} \therefore \quad R_p=3 \Omega$
(a) Current reading on the ammeter ( I $)=\frac{ E }{ R + r }=\frac{2}{(0.8+3)+1.2}=\frac{2}{5}=0.4 A$.
(b) $I =\frac{ E - V }{r} \Rightarrow 0.4=\frac{2- V }{1.2} \Rightarrow 0.48=2- V$
$\therefore$ Potential difference $( V )=2-0.48=1.52 V$.

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Question 32 Marks

Consider mentioned figure alongside and calculate equivalent resistance between
(a) Points A and B
(b) Points B and C
(c) Points A and C

Answer

(a) Equivalent resistance between A and B
$\frac{1}{R p_1}=\frac{1}{4}+\frac{1}{12}=\frac{3+1}{12}=\frac{4}{12}=\frac{1}{3} ; \quad \therefore R p_1=3 \Omega$
(b) Equivalent resistance between B and C
$\frac{1}{R_2}=\frac{1}{12}+\frac{1}{24}+\frac{1}{8}=\frac{2+1+3}{24}=\frac{6}{24}=\frac{1}{4} ; \quad \therefore RP_2=4 \Omega$
(c) Equivalent resistance between A and C
$R_{S}=3+4=7 \Omega$

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Question 42 Marks

State the factors on which internal resistance of a cell depends.

Answer

The internal resistance of a cell
(i) is inversely proportional to the surface area of electrodes in contact with the electrolyte.
(ii) is directly proportional to the distance between the electrodes of the cell.
(iii) depends on nature, concentration and temperature of the electrolyte.

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Question 52 Marks

(a) State Ohm's law.
(b) What are the limitations of Ohm's law?

Answer

(a) According to Ohm's law, the current flowing through a conductor is directly proportional to the potential difference across its ends, provided the physical conditions of the conductor remains the same.
(b) Certain resistors such as diodes, triodes, semiconductors, do not obey Ohm's law. For these resistors, the V-I graph is not a straight line. Also, Ohm's law is valid as long as the temperature of the conductor is constant.

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Question 62 Marks

(a) State three characteristics of a series circuit.
(b) State three characteristics of a parallel circuit

Answer

(a) (i) Magnitude of current through each resistor is same.
(ii) There is a contimuous drop in the potential all along the series circuit.
(iii) Potential difference across the entire circuit is equal to the sum of potential differences across each of the individual resistors.
(b) (i) Potential difference across all the resistors in a parallel circuit is a constant quantity.
(ii) Current divides in different resistors in the inverse ratio of the resistances of the parallel circuit. It means a low resistance allows more current and vice-verse.
(iii) Sum of currents in the individual resistors is equal to the total current following into parallel circuit.

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Question 72 Marks

Calculate the equivalent resistance between $P$ and $Q$ in the following diagram.

Answer

Resistance of two $10 \Omega$ resistance in series, their equivalent resistance $\left(R_1\right)=10+10=20 \Omega$
Equivalent resistance of $20 \Omega\left( R _1\right)$ in parallel with $5 \Omega$ resistance,
$\frac{1}{R_2}=\frac{1}{20}+\frac{1}{5}=\frac{1+4}{20}=\frac{5}{20}=\frac{1}{4} \quad \Rightarrow R_2=4 \Omega$
$\therefore$ Equivalent resistance between P and $Q =3 \Omega+ R _2+3 \Omega=3 \Omega+4 \Omega+3 \Omega=10 \Omega$

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Question 82 Marks

(a) The V-I graph for a series combination and for a parallel combination of two resistors is as shown in the figure below. Which of the two A and B represents the parallel combination?
(b) A cell of e.m.f. 1.5 V is comnected to an external resistance of $2 \Omega$, when the p.d. recorded is 1.2 V . Calculate the internal resistance of cell.

Answer

(a) The graph line A represents parallel combination.
(b) $I =\frac{ E }{ R +r}=\frac{1.5}{2+r}$........(i)
Now, $V = IR$
$\begin{array}{l}\Rightarrow 1.2=\frac{1.5}{2+r} \times 2 \quad \text { [Putting the value of I from equ. (i)] } \\
\Rightarrow 2+r=\frac{1.5 \times 2}{1.2}=2.5 \\
\therefore r=2.5-2=0.5\end{array}$
Thus, internal resistance of cell $=0.5 \Omega$

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Question 92 Marks

(a) What do you understand by the term ohmic resistance?
(b) A wire of length 120 cm and area of cross-section $0.2 cm^2$ offers a resistance of $4 \Omega$. Calculate the specific resistance of the wire.

Answer

(a) A resistor, which obeys Ohm's law, is said to have ohmic resistance.
(b) Given, $I=120 cm=1.2 m, a=0.2 cm^2=0.2 \times 10^{-4} m^2, R =4 \Omega$
Thus, specific resistance $(\rho)=\frac{ R \times a}{l}$
$\begin{array}{l}=\frac{4 \Omega \times 0.2 \times 10^{-4} m^2}{1.2 m}=\frac{2}{3} \times 10^{-4} \Omega m \\
=0.667 \times 10^{-4} \Omega m=6.67 \times 10^{-5} \Omega m\end{array}$

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Question 102 Marks

(a) State the SI unit of specific resistance.
(b) Four resistance A, B, C and D of resistance $3 \Omega$ each are joined to form a square. Calculate the equivalent resistance between the opposite ends of the square

Answer

(a) The SI unit of specific resistance is ohm-metre ( $\Omega- m )$.
(b) Resistance of $A$ and $B$ in series, $R_1=3+3=6 \Omega$ Resistance of C and D in series, $R _2=3+3=6 \Omega$
$\therefore$ Resistance of $R _1$ and $R _2$ in parallel,
$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}=\frac{1}{6}+\frac{1}{6}=\frac{2}{6}=\frac{1}{3}$
$\therefore$ Equivalent resistance $(R)=3 \Omega$

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Question 112 Marks

State the laws of resistance.

Answer

Laws of resistance -
(i) Resistance of a conductor depends upon its nature of material.
(ii) Resistance of a conductor is directly proportional to its length (R $\propto l$ ).
(iii) Resistance of a conductor is imversely proportional to its area of cross-section, $\left( R \propto \frac{1}{ a }\right)$.

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Question 122 Marks

Define electric potential. State its practical unit and define it.

Answer

The amount of work done in moving a unit positive charge from infinity to a given point in an electric field is called electric potential.
The unit of electric potential is volt. It is denoted by the symbol V.
One volt is defined as the electric potential at a point when 1 J of work is done in bringing 1 C of electric charge from infinity to the given point in an electric field.

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Question 132 Marks

(a) Define the term potential. State its SI unit.
(b) The V-I graph for a series combination and for a parallel combination of two resistors is as shown in the figure. Which of the two A or B represents the parallel combination? Give a reason for your answer.

Answer

(a) The amount of work done (energy spent) in moving a unit positive charge from infinity to a given point in an electric field is called electric potential. SI unit of electric potential is volt (V).
(b) The graph line A represents parallel combination. It is because, in parallel combination, the magnitude of resistance decreases and hence, the current in the circuit increases.

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Physics [2 Mark Question Answer]

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