Find the maximum power transferred to the load resistance (R_{L}).

Option 2 : 2.5 W

CT 1: Network Theory 1

11667

10 Questions
10 Marks
10 Mins

__Concept__:

The maximum power theorem for DC circuit states that, when the load resistance RL equals the Thevenin equivalent resistance across RL, maximum power is transferred to the load.i.e.

When RL = Rth, maximum power is transferred to the load.

The maximum power is given by:

\(P(max)=\frac{V_{th}^2}{4R_{th}}\)

__Calculation__:

For the given circuit, Rth = 10 Ω and Vth = 10 V

The maximum power transferred to the load will be:

\(P(max)=\frac{V_{th}^2}{4R_{th}}=\frac{(10)^2}{4× 10}\)

**P(max) = 2.5 W**

Even if we don't remember the formula for the maximum power, we can solve the circuit for calculating it, i.e.

For maximum power transfer, RL = Rth,

So, RL = 10 Ω

Now the current through the circuit will be:

\(I=\frac{10}{10 + 10}= 0.5~A\)

Power at the load will be:

PL = I2 R

**PL = (0.5)2 × 10 = 2.5 W**

This is nothing but the maximum power that could be transferred to the load.