Question
In the circuit shown, the cells $$A$$ and $$B$$ have negligible resistances. For $${V_A} = 12\,V,{R_1} = 500\,\Omega $$ and $$R = 100\,\Omega $$ the galvanometer $$\left( G \right)$$ shows no deflection. The value of $${V_B}$$ is
In the circuit shown, the cells $$A$$ and $$B$$ have negligible resistances. For $${V_A} = 12\,V,{R_1} = 500\,\Omega $$ and $$R = 100\,\Omega $$ the galvanometer $$\left( G \right)$$ shows no deflection. The value of $${V_B}$$ is
A.
$$4\,V$$
B.
$$2\,V$$
C.
$$12\,V$$
D.
$$6\,V$$
Answer :
$$2\,V$$
Solution :
If potential difference across $$R\,\Omega $$ resistor is equal to potential difference of cell $$B,$$ galvanometer shows no deflection.
Applying Kirchhoff's law, $$500I + 100I = 12$$
So, $$I = \frac{{12 \times {{10}^{ - 2}}}}{6} = 2 \times {10^{ - 2}}A$$
Hence, $${V_B} = 100\left( {2 \times {{10}^{ - 2}}} \right) = 2\,V$$
If potential difference across $$R\,\Omega $$ resistor is equal to potential difference of cell $$B,$$ galvanometer shows no deflection.
Applying Kirchhoff's law, $$500I + 100I = 12$$
So, $$I = \frac{{12 \times {{10}^{ - 2}}}}{6} = 2 \times {10^{ - 2}}A$$
Hence, $${V_B} = 100\left( {2 \times {{10}^{ - 2}}} \right) = 2\,V$$
