Solving Simple Capacitors Homework: Q, V, E

[HZXAHNLfzjSr]

Homework Statement

A voltmeter of resistance 150kilo Ohms is connected across a 50 micro F capacitor. If at time t= 0 the voltmeter reading is 20V. Find

a) charge on capacitor at time t=o
b) voltmeter reading after 10s
c) the time which must elapse after t = o before 95% of the energy stored has been dissipated

Homework Equations

Q=cv
E=1/2 cv^2

The Attempt at a Solution

a) I used Q = cv
b) I used V = (Vo)(e) - (t/RC) formula but not getting the correct answer
c) I tried a bunch of things but didn't even get close to the answer.

So can someone show me how to solve (b) and (c).

Thanks!

 

[HZXAHNLfzjSr]

Also can someone tell me if it's

V = (Vo)(e) - (t/RC)

OR

V = (Vo)(e) ^ - (t/RC)

In the latter case, kindly explain how I'd solve this to get V.

Thanks!

 

[N-Gin]

Also can someone tell me if it's

V = (Vo)(e) - (t/RC)

OR

V = (Vo)(e) ^ - (t/RC)

In the latter case, kindly explain how I'd solve this to get V.

Thanks!

It's the second equation

$$V=V_{0}e^{-\frac{t}{RC}}.$$

(It's easy to see that first one is wrong - it's dimensionally incorrect!)

If you know what is $V_{0}$, you know everything you need to solve the problem completely.

 

[rsalmon]

If you know what is $V_{0}$, you know everything you need to solve the problem completely.

You said that V0 is 20 volts and also be careful with the dimensions (kilo and micro etc).

part c) requires you to rearrange to get it in terms of t. Also you have to work out V (hint: voltage is 'energy per unit charge')

 

[HZXAHNLfzjSr]

Well I am still unsure as to how to do part (c) :(

Can someone show me the steps?

Thanks!

 

[N-Gin]

For the c) part, just use the formula

$$E(t)=\frac{1}{2}CV^{2}(t).$$

It must be equal to 5% percent of the initial energy

$$E_{0}=\frac{1}{2}CV_{0}^{2}.$$

 

[HZXAHNLfzjSr]

Thanks I figured it out and just confirmed it with your posts ;)