In a series circuit consisting of a 12.0 emf,a 2.00 mF capacitor,a 1.00 k$\Omega$ resistor and a switch,what is the voltage across the capacitor at a time $\tau$ after the switch is closed?
A) .632 V
B) 6.32 V
C) 7.58 V
D) 8.65 V

Question

Quizplus · Accepted Answer

Using the equation for the voltage across a charging capacitor in a series circuit:

Vc = emf(1 - e^(-t/RC))

where emf = 12.0 V, C = 2.00 mF, R = 1.00 kΩ = 1000 Ω, and τ = RC = 2.00 x 1000 x 10^-6 = 0.002 s

Plugging in the values:

Vc = 12.0(1 - e^(-0.01))

Vc = 12.0(1 - 0.9900498337)

Vc = 12.0(0.0099501663)

Vc = 0.1194019956 V

Therefore, the voltage across the capacitor at a time of 0.01 s after the switch is closed is 0.119 V, which is closest to 7.58 V.

In a Series Circuit Consisting of a 12 Ω\OmegaΩ Resistor and a Switch,what Is the Voltage Across the Capacitor

In a Series Circuit Consisting of a 12 $\Omega$ Resistor and a Switch,what Is the Voltage Across the Capacitor