Two identical circular rings having resistance $12\Omega$ each are placed in such a way that they cross each other's centres $C_1$ and $C_2$ as shown. They are joined at intersection points $P$ and $Q$ through conducting joints. Terminal $P$ and $Q$ are connected to the circuit having battery of EMF $10 \mathrm{V}$ as shown

For the portion of the circuit shown in figure, all the voltmeters are identical and reading of voltmeter $V_1$ and $V_2$ are $10 \mathrm{V}$ and $5 \mathrm{V}$ respectively, then

For the circuit shown in figure, capacitor is initially charged to potential of $5 \mathrm{V}$. Now switch $S$ is closed at $t=0$ and at time $t=t_0$ potential across $AB$ is found to be $\frac{35}{3} \mathrm{V}$, then

In the arrangement of meter bridge, wire $AB$ is of length $60 \mathrm{cm}.$ The null point is at distance $x$ from $A$. Find the value of $x$ in $\mathrm{cm}.$

A galvanometer of resistance $50\Omega$ shows full scale deflection at $100\mu A.$ The resistance of shunt to be used to make it an ammeter of range $0-2A$ is $x\times {10}^{-4} \mathrm{m\Omega }$. Find the value of $x$ as the nearest integer.

(Give the answer to the nearest integer in $...\times {10}^{-4}$)