Calculating Capacitor Charge and Energy: A Quick Guide

[CharlieBewn]

Homework Statement

A capacitor with C = 4600 μ F is fully charged using a 12 V power supply.
At time t = 0, you start discharging the capacitor via a 50 k Ω resistor.
Calculate the initial charge Q max (in mC) and the initial energy E max (in mJ) stored in the capacitor.

Then, calculate the residual charge Q, the potential difference V across the capacitor and its energy E content after 49 seconds.
Q=mC
V=V
E=mJ

Have to answer in decimal numbers to 2 sig fig.

Homework Equations

The Attempt at a Solution

Here’s my attempt:
Q max = CV = 4600 uF * 12 V = 55200 u coulomb = 55.2 mC
E max = 1/2 CV^2 = 1/2 4600 uF (12 V)^2 = 331.2 mJ

tau = RC = 50e3*4600e-6 = 230 S.

Q = Q max exp(-t/tau) = 55.2 mC * exp(-49/230) = 55.2 mC * 0.808121 = 44.6 mC.
V = V power supply * 0.808121 = 12 * 0.808121 = 9.697 V
E = 1/2 CV^2 = 1/2 4600 uF (9.697 V)^2 = 216.3 mJ


Is this looking correct?
The only thing i can't do (stupid i know) is convert these to 2 sig fig whilst also in decimal form. For example V = 9.697 is 9.7
Is it 55.2 = 50.2
331.2 = 330.0
44.6 = 45.0
216.3 = 210.0

 

[marcusl]

It looks right. See this for rounding:
http://en.wikipedia.org/wiki/Significant_digits

 

[tiny-tim]

Welcome to PF!

or https://www.physicsforums.com/library.php?do=view_item&itemid=523