LR circuits: A series LR circuit consists of a 2.0-H inductor with negligible internal resistance, a 100-ohm resistor, an open switch, and a 9.0-V ideal power source. After the switch is closed, what is the maximum power delivered by the power supply?
A) 0.40 W
B) 81 W
C) 0.090 W
D) 8.1 W
E) 0.81 W

Question

Quizplus · Accepted Answer

The maximum power delivered by the power supply occurs when the circuit reaches its steady state, where the current through the circuit is constant. In a series LR circuit, the current reaches its maximum value (I_max) when the inductor has reached its maximum current (I_Lmax), which occurs when the voltage across the resistor is equal to the voltage across the inductor (V_R = V_L).

We can use Ohm's law to find I_max: 
V = IR + VL 
9.0 V = I(100 Ω) + (2.0 H)(dI/dt)

At the maximum current, dI/dt = 0, so we have: 
I_max = V/R = 9.0 V/100 Ω = 0.090 A

The maximum power delivered by the power supply is given by: 
P_max = V^2/R = (9.0 V)^2/100 Ω = 0.81 W

Therefore, the correct answer is (E) 0.81 W.

LR Circuits: a Series LR Circuit Consists of a 2