If a source has no reactance, maximum power transfer occurs when the load resistance equals the source resistance.

If a source has no reactance, maximum power transfer occurs when the load resistance equals the source resistance.

• A. True
• B. False
• C. Only with DC
• D. Only with AC

Answer: (A)

Maximum power transfer occurs when the load is matched to the source impedance. If the source has no reactance, its impedance is purely real, Zs = Rs. Model the source as an ideal voltage Vth in series with Rs and the load as Rl. The power delivered to the load is P = Vth^2 Rl /(Rs + Rl)^2. To find the maximum, treat P as a function of Rl and differentiate: dP/dRl is proportional to (Rs − Rl)/(Rs + Rl)^3. Setting this to zero gives Rl = Rs, which yields the peak power. This result does not depend on whether the excitation is DC or AC, as long as the source has zero reactance, so the condition applies to both. Therefore, the statement is true.

Maximum power transfer occurs when the load is matched to the source impedance. If the source has no reactance, its impedance is purely real, Zs = Rs. Model the source as an ideal voltage Vth in series with Rs and the load as Rl. The power delivered to the load is P = Vth^2 Rl /(Rs + Rl)^2. To find the maximum, treat P as a function of Rl and differentiate: dP/dRl is proportional to (Rs − Rl)/(Rs + Rl)^3. Setting this to zero gives Rl = Rs, which yields the peak power. This result does not depend on whether the excitation is DC or AC, as long as the source has zero reactance, so the condition applies to both. Therefore, the statement is true.