Question

Find the value of RL for maximum power transfer in the following circuit.

a) RL = R/2
b) RL = R
c) RL = 2R
d) RL = √2R

Answer 1

The value of RL for maximum power transfer in the circuit is RL = R.

Step-by-step explanation:

The maximum power transfer theorem states that the maximum power is transferred from a source to a load when the resistance of the load is equal to the internal resistance of the source. In this circuit, the internal resistance of the source is R. Therefore, the value of RL for maximum power transfer is b) RL = R.

Answer 2

In an RLC series circuit, the value of RL for maximum power transfer is when c) RL = 2R

Step-by-step explanation:

In order to find the value of RL for maximum power transfer in a circuit, we need to consider the concept of impedance.

Impedance is a measure of the opposition to the flow of current in an AC circuit, and it includes both resistance (R) and reactance (X).

For maximum power transfer, the impedance of the load (RL) should be equal to the complex conjugate of the total impedance of the circuit (ZT).

Using the formula for the total impedance of an RLC series circuit: ZT = R + j(XL - XC)

Where

XL is the inductive reactance

XC is the capacitive reactance

We can calculate the impedance at different values of RL.

Calculating the total impedance at different values of RL, we find:

For RL = R/2: ZT = R + j(2L - 2C)

For RL = R: ZT = R + j(0)

For RL = 2R: ZT = R + j(2C - 2L)

For RL = √2R: ZT = R + j(XL - XC)

Based on the above calculations, we can conclude that the correct answer is c) RL = 2R. This is because at RL = 2R, the total impedance of the circuit will be purely resistive, resulting in maximum power transfer.