Question

State Kirchhoff's laws and use them to obtain the condition for balance of a Wheatstone bridge.

Hint:

Kirchhoff’s Laws: KCL (sum of currents at junction) and KVL (sum of voltages around a loop = 0). Wheatstone bridge balance condition: \(\frac{R_1}{R_2} = \frac{R_3}{R_4}\).

Answer 1

Kirchhoff's Laws:
1. Kirchhoff's Current Law (KCL): This law states that the total current entering a junction is equal to the total current leaving the junction. Mathematically, \[ \sum I_{\text{in}} = \sum I_{\text{out}} \] This law is a consequence of the conservation of charge.
2. Kirchhoff's Voltage Law (KVL): This law states that the sum of all voltages around any closed loop in a circuit is zero. Mathematically, \[ \sum V_{\text{across elements}} = 0 \] This law is a consequence of the conservation of energy in electrical circuits.
Balance of a Wheatstone Bridge:
The Wheatstone bridge consists of four resistors arranged in a diamond shape, with a battery providing a potential difference. The condition for balance occurs when the ratio of resistances in one arm equals the ratio in the opposite arm. Let the resistors in the four arms of the bridge be \(R_1, R_2, R_3, R_4\), with \(R_1\) and \(R_2\) forming one pair of opposite arms and \(R_3\) and \(R_4\) forming the other pair. A galvanometer is connected between the midpoints of the two arms. The balance condition for the bridge is: \[ \frac{R_1}{R_2} = \frac{R_3}{R_4} \] In the balanced state, no current flows through the galvanometer. Using Kirchhoff's laws, we can derive this condition by applying KCL and KVL to the loops in the circuit. The condition for no current through the galvanometer is equivalent to the ratio of resistances being equal.
In summary, Kirchhoff's laws provide the basis for analyzing electrical circuits, and the balance condition for a Wheatstone bridge is given by \(\frac{R_1}{R_2} = \frac{R_3}{R_4}\).