Answer to Question #226818 in Electricity and Magnetism for Ndilloh

Question

We keep the switch at position x for a sufficient time and thereafter (at t0) connect it to y, in the cercuit shown below : what amount will be measured through the resistor after 5.0 micro-seconds from t0, if v=9v, R= 10ohms and c=1 micro F

Answer 1

Given:

$R=10\:\Omega$

$C=1*10^{-6}\:\rm F$

$V=9\:\rm V$

$t=5*10^{-6}\:\rm s$

The time constant

$$\tau=RC=10*1*10^{-6}=10^{-5}\:\rm 1/s$$

The current through the resistor

$$I=\frac{V}{R}e^{-t/\tau}$$

$$I=\frac{9}{10}e^{-5*10^{-6}/10^{-5}}=0.55\:\rm A$$

The voltage

$$V_R=I*R=0.55*10=5.5\:\rm V$$