A 20.0-μF capacitor is charged to 200 V and is then connected across a 1000-Ω resistor. What is the initial current just after the capacitor is connected to the resistor?

Question

Quizplus · Accepted Answer

The initial current just after the capacitor is connected to the resistor can be found using the formula:

i = V/R(1-e^(-t/RC))

Where:
V = 200 V (voltage across the capacitor)
R = 1000 Ω (resistance of the resistor)
C = 20.0 μF (capacitance of the capacitor)

Assuming that the time constant is small enough such that the voltage across the capacitor remains constant during discharge through the resistor, t can be assumed to be 0.

Substituting the given values:

i = 200/1000(1-e^(-0/20x10^-6x1000)) 
i = 200/1000(1-e^0) 
i = 200/1000(1-1) 
i = 0

This means that the initial current just after the capacitor is connected to the resistor is 0, since the capacitor acts as an open circuit initially. However, if we assume that a non-zero current flows through the resistor at t=0, then we can use the formula:

i = V/R

Substituting the given values:
i = 200/1000 
i = 0.2 A or 200 mA

Therefore, the best choice is B, 200 mA.

A 200-μF Capacitor Is Charged to 200 V and Is Then