Find the equivalent resistance between point $A$ and $B$ in the following circuit. (The resistance of each resistor is $R$ )

In a meter bridge the balancing length from the left end is found to be 25 cm . The value of the unknown resistance is (assume, standard resistance of $1 \Omega$ is in the right gap)

Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. A point $P$ at a distance $y$ away from the wire carrying current $i$ is shown in the figure. If the magnetic field is zero at point $P$, then the magnitude of $i$ is

A solenoid of length 2 m carries a current of 20 A . The diameter of the solenoid is 3 cm . If the magnetic field inside the solenoid is 20 mT , then the length of wire forming the solenoid is (assume, $\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ )