A capacitor discharge circuit of time constant 45ms includes a capacitor and resistor. The capacitor has a capacitance of 18µF What is the resistance of the resistor?

This question is in one of the CIE Physics Pre-U sample papers, and if you know the definition of the time constant for a capacitor circuit (=RC), its very easy, however even if you didnt it canbe derived fairly easily.

Consider a circuit containing just a capacitor C and resistor R, with the capacitor initially storing some charge Q0 with a voltage V0 across it. Call the curent flowing i, the voltage across the capacitor as time progresses Vc and the changing charge Q. By Kirchoff's law,

Vc + iR=0

Then we know that dQ/dt = i and C=Q/Vc, so we can say:

Q/C + RdQ/dt=0 and so RCdQ/dt + Q=0 

This has solution Q=Q0exp(-t/RC) and comparing this with the standard form of a time decaying property, X=X0exp(-t/k), where k is the time constant, gives k=RC, and then the problem is trivial.

Answered by Sam C. Physics tutor

5256 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

How do you prove Kepler's Third Law?


A light wave has a wavelength of 420nm, calculate the energy of this wave in joules.


How do capacitors work and what are its units?


Explain how resonance occurs for a driven oscillating system and describe the effect of damping on the resonant frequency.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences