Question

Output remains half of input when output resistance is

• A. \(\frac{R}{4}\)
• B. \(\frac{R}{6}\)
• C. \(\frac{R}{2}\)
• D. \(\frac{R}{8}\)

Hint:

Maximum power transfer occurs when load equals source resistance.

Answer 1

The Correct Option is C

Concept: Voltage divider: \[ V_o = \frac{R_L}{R + R_L} V_i \]

Step 1: Given condition \[ V_o = \frac{1}{2} V_i \]

Step 2: Substitute \[ \frac{R_L}{R + R_L} = \frac{1}{2} \]

Step 3: Solve equation \[ 2R_L = R + R_L \]

Step 4: Simplify \[ R_L = R \]

Step 5: Interpretation Equivalent output resistance = \(R/2\).

Final Answer: \[ \boxed{\frac{R}{2}} \]