Question

The Wheatstone bridge shown in the diagram is balanced. If P3 is the power dissipated by R3 and P1 is the power dissipated by R1, then the ratio P3/P1 is: 

• A. K/L
• B. K2/L
• C. L/K2
• D. L/K

Answer 1

The Correct Option is A

To solve the problem, we need to find the ratio of power dissipated by resistors $R_3$ and $R_1$ in a balanced Wheatstone bridge circuit.

1. Power Dissipation in Resistor:
The power dissipated by a resistor is given by:
$ P = \frac{V^2}{R} $
In a balanced Wheatstone bridge, no current flows through the galvanometer, and the potential drop across $R_1$ and $R_3$ can be related to their positions in the bridge.

2. Balanced Wheatstone Bridge Condition:
For a balanced bridge:
$ \frac{R_1}{R_2} = \frac{R_3}{R_4} $
In the given diagram, resistors $R_1$ and $R_3$ are on opposite arms, with resistors labeled $L$ and $K$ in the corresponding branches.
So, assume:
- $R_1 = L$,
- $R_3 = K$

3. Power Ratio:
Using $P = \frac{V^2}{R}$ and assuming the same voltage across each arm (due to balance), we get:
$ \frac{P_3}{P_1} = \frac{V^2 / R_3}{V^2 / R_1} = \frac{R_3}{R_1} = \frac{K}{L} $

Final Answer:
The ratio $ \frac{P_3}{P_1} $ is K / L .