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The resistance per centimeter of a meter bridge wire is $\mathrm{r}$, with $\mathrm{X}\ \Omega$ resistance in left gap. Balancing length from left end is at $40 \mathrm{~cm}$ with $25\ \Omega$ resistance in right gap. Now the wire is replaced by another wire of $2 \mathrm{r}$ resistance per centimeter. The new balancing length for same settings will be at
In the figure, the potentiometer wire $AB$ of length $L$ and resistance $9r$ is joined to the cell $D$ of $emf$ $\varepsilon $ and internal resistance $r$. The cell $C's$ $emf$ is $\frac{\varepsilon }{2}$and its internal resistance is $2r$. The galvanometer $G$ will show no deflection when the length $AJ$ is
Across a metallic conductor of non-uniform cross section a constant potential difference is applied. The quantity which remains constant along the conductor is
The electric current through a wire varies with time as $I=I_0+\beta t$. where $I_0=20 \mathrm{~A}$ and $\beta=3 \mathrm{~A} / \mathrm{s}$. The amount of electric charge crossed through a section of the wire in $20 \mathrm{~s}$ is :
When the resistance $R$ (indicated in the figure below) is changed from $1 \,k \Omega$. to $10 \,k \Omega$, the current flowing through the resistance $R'$ does not change. What is the value of the resistor $R'?$
In the circuit shown, the resistances are given in ohms and the battery is assumed ideal with $\mathrm{emf}$ equal to $3.0$ $\mathrm{volts}.$ The resistor that dissipates the most power is
A potential divider is used to give outputs of $4\,V$ and $8\,V$ from a $12\,V$ source. Which combination of resistances, $(R_1 : R_2 : R_3)$ gives the correct voltages
The ratio of the equivalent resistance of the network (shown in figure) between the points $a$ and ${b}$ when switch is open and switch is closed is ${x}: 8 .$ The value of ${x}$ is ..... .