Question

In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of resistor R will be

• A. 100 $\Omega$
• B. 200 $\Omega$
• C. 1000 $\Omega$
• D. 500 $\Omega$

Answer 1

The correct option is A 100 $\Omega$

Applying Kirchhoff's law
for loop BCDFAEB: $500i=12-2\Rightarrow i=10/500=1/50$
when galvanometer shows zero deflection then no current flow through it.
now for loop BCDEB: $500i+Ri=12\Rightarrow i=\frac{12}{R+500}$
or $1/50=12/(R+500)$
or $R+500=600\Rightarrow R=100\Omega$