Question

In the given circuit, if the cell delivers maximum power to the circuit, then value of $R$ is

• A. $\dfrac{4}{9} \ \Omega$
• B. $8 \ \Omega$
• C. $2 \ \Omega$
• D. $4 \ \Omega$

Hint:

Apply the maximum power transfer theorem: $R_{\text{load}} = R_{\text{Thevenin}}$

Answer 1

The Correct Option is C

According to the maximum power transfer theorem, maximum power is delivered to the load when the load resistance $R$ is equal to the Thevenin resistance of the rest of the circuit.
Looking at the circuit, the internal resistors form a combination that can be simplified to find Thevenin equivalent resistance across the terminals where $R$ is connected.
Using proper reduction and simplification of the internal network, we get $R_{\text{Thevenin}} = 2\ \Omega$.
Thus, for maximum power transfer, $R = R_{\text{Thevenin}} = 2 \ \Omega$