1 Show from the definitions of R and Cthat the product RChas

1. Show from the definitions of R and Cthat the product RChas the units of time. This problem is an example of dimensional analysis, e.g. had we asked you to show that acceleration multiplied by time had the units of speed, you would look in a textbook to find that the units of a are m/sec then, if you multiplied (m/sec by seconds, you would get sec, which are the units of a speed. An uncharged capacitor and a resistor are connected in series to a battery. If CJ5.0 mF and R 4.0x105 2, find the time constant of the circuit. Show all of your calculations.

Solution

1)

R = resistance

Now, R = V/I

V = voltage

I = current

Now, I = charge/time = Q/t

So, R = V*t/Q

Now, Capacitance, C = charge across the capacitor/voltage across it = Q/V

Now, C*R = (Vt/Q)*Q/V = t <------------ it has the dimensions of time <==== PROVED

2)

time constant, T = R*C

= 4*10^8*5*10^-3

= 2*10^6 s