Question

an ideal voltage of 5V is atached in between an unbalaced wheatstone bride of 1ohm and 3ohm with external resistance of R connected across the setup. what value of R ensures max power thru the circuit

• A. 0.25 Ω
• B. 0.50 Ω
• C. 0.75 Ω
• D. 1.00 Ω

Answer 1

Answer: (C)

R = 0.75 Ω

Answer 2

To maximize the power delivered to $R$, by the Maximum Power Transfer Theorem, the load resistance must equal the Thevenin resistance seen from its terminals.

1. Find Thevenin Resistance: Replace the voltage source by a short. The node (where $R$ connects) now “sees” two resistors: one from the node to 5 V terminal (now at 0 V) is 1 Ω and from the node to ground is 3 Ω. These are in parallel:

   $$R_{th} = \frac{1 \times 3}{1 + 3} = \frac{3}{4} = 0.75\ \Omega.$$

2. Maximum Power Transfer: By setting $R = R_{th} = 0.75\ \Omega$, the load receives maximum power.