A capacitor of capacitance `10 muF` is connected to an oscillator giving an output voltage `epsilon = (10 V) sin omegat`. Find the peak currents in the circuit for `omega = 10 s^(-1), 100 s^(-1), 500 s^(-1), 1000 s^(-1)`.

Explanation

Here `C=10 mu F = 10 xx 10^(-6) F`
`=10 ^(-5) F`
`E= (10V) sin omega t`
`omega = 10 s^-1`
(a) `i= (E_0)/(1//omegaC) = (10)/(1//10 xx 10^-5)A`
`=1 xx 10^-3 A`
(b) omega `= 100 s^-1`
`i= (E_0)/(1//omega C)=(10)/(1//100 xx 10^-5)`
`=10/10^3 = 1 xx 10^-2 A`
`=0.01A`
(c) ` omega = 500 s^-1`
`i=(E_0)/(1//omegaC)=10/(1//500 xx 10^-5)`
`=10 xx 500 xx 10^-5`
`=5xx 10^2 A=0.05A`
(d) `omega = 1000 s^-1`
`i= (10)/(1//1000 xx 10^-5)`
`=10 xx 1000 xx 10^-5`
`=10^-1 A = 0.1A`