Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

PRACTICE IT! An uncharged capacitor and a resistor are connected in series to a

ID: 1539235 • Letter: P

Question

PRACTICE IT!

An uncharged capacitor and a resistor are connected in series to a battery, as shown in the figure above. If e m f = 15.0 V, C = 5.50 µF, and R = 7.90 105 , find the following.

(a) the time constant of the circuit

4.375s

(b) the maximum charge on the capacitor

82.5µC

(c) the charge on the capacitor after 5.50 s

59.03µC

(d) the potential difference across the resistor after 5.50 s

-4.267 V

(e) the current in the resistor at that time

5.4e-6.

Use the values from PRACTICE IT to help you work this exercise.

(a) Find the charge on the capacitor after 2.10 s have elapsed.

Q = C

(b) Find the magnitude of the potential difference across the capacitor after 2.10 s.

VC = V

(c) Find the magnitude of the potential difference across the resistor at that same time.

VR = V

Explanation / Answer

a)The magnitude if charge after time t is given by:

Q = CVb (1 - e^-t/RC)

Vb is the battery voltage

RC = 7.9 x 10^5 x 5.5 x 10^-6 = 4.345 s

Q = 5.5 x 10^-6 x 15 (1 - e^-2.1/4.345)

Q = 31.62 x 10^-6 = 31.62 micro C

Hence, Q = 31.62 micro C

b)V = V0 (1 - e^-t/RC)

V = 15 (1 - e^-2.1/4.345) = 5.75 Volts

Hence, V = 5.75 Volts

c)The drop across the resistor would be:

Vr = emf - V = 15 - 5.75 = 9.25 V

Hence, V = 9.25 Volts

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote