Question

In the given electrical network, the value of resistance ' $R$ ' when the current in the galvanometer will be zero, is

• A. $4\Omega$
• B. $6\Omega$
• C. $7\Omega$
• D. $10\Omega$

Hint:

Whenever a galvanometer current is zero in a bridge circuit, immediately think of the balanced bridge condition: \[ \frac{P}{Q}=\frac{R}{S} \] Then identify the four arms carefully from the diagram before solving.

Answer 1

The Correct Option is B

The potential difference across the resistance \(R\) is \(6\,\text{V}\).
Using Ohm’s law,

\[ i=\frac{V}{R} \]

From the circuit,

\[ i=\frac{10-6}{4} \]

\[ i=\frac{4}{4}=1\,\text{A} \]

Again using Ohm’s law for resistance \(R\),

\[ V=iR \]

Substituting the values,

\[ 6=1\times R \]

Therefore,

\[ R=6\,\Omega \]

Final Answer:

\[ \boxed{6\,\Omega} \]