In the given electrical circuit of Wheatstone bridge, currents and the resistances are shown. Apply the Kirchhoff’s law to the mesh ADCEA to establish a correct relation between the currents I2 and Ig.
Choose the correct option from the following:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 13 I_2 + I_g = 2 \)
Kirchhoff’s loop rule: around a closed loop, the sum of the potential drops across the resistors equals the emf in the loop.
Readings from the figure for the loop ADCEA:
\( A \to D:\ 60\,\Omega,\ \text{current } I_2 \)
\( D \to C:\ 5\,\Omega,\ \text{current } I_2 + I_g \)
\( \text{emf of the cell} = 10\,\mathrm{V} \)
\( \displaystyle 60 I_2 + 5 (I_2 + I_g) = 10 \)
\( \displaystyle 65 I_2 + 5 I_g = 10 \)
Dividing by 5:
\( \displaystyle 13 I_2 + I_g = 2 \)