Question

In the given network, calculate: 
(i) Effective resistance between points A and M, and 
(ii) Power supplied by the battery. 

Hint:

For complex circuits, simplify step by step, combining resistors in series and parallel to reduce the circuit to a simpler equivalent form. This approach helps in calculating the total resistance and subsequently the power supplied by the battery.

Answer 1

Calculation of Effective Resistance and Power Supplied 
 

1: Analyzing the Circuit
The given circuit consists of resistors in series and parallel. First, simplify the resistances step by step. 1. Combine the 10\(\mu\) and 10\(\mu\) resistors in parallel between points B and C: \[ R_{\text{BC}} = \frac{1}{\frac{1}{10} + \frac{1}{10}} = 5 \] 2. Combine the 20\(\mu\) resistors in parallel between points C and D: \[ R_{\text{CD}} = \frac{1}{\frac{1}{20} + \frac{1}{20}} = 10 \] 3. Simplify the overall network of resistors to find the effective resistance between points A and M: \[ R_{\text{eff}} = 12 \] 

2: Power Supplied by the Battery
The power supplied by the battery is given by: \[ P = \frac{V^2}{R_{\text{eff}}} = \frac{6^2}{12} = 3W \] Thus, the power supplied by the battery is \( P = 3W \).