Question

(1 point) A 86 4F capacitor is connected to a source that operates at 70 Hz with a peak potential difference of 18 V. Find: a) the peak current: A b) the current when the potential difference has its peak value: A c) the current when the potential difference has one-half the (positive) peak value (there are two answers, list them in increasing order): A A d) the instantaneous power delivered to the capacitor at 5 ms. W

Answer 1

The source voltage is

V(t) = Vosin (27 ft)

and current is

$I(t)=\frac{V_{0}}{1/wC}sin(2\pi ft+\pi /2)$

(a) The peak current is

VO 10 1/wC

$I_{0}=18*2\pi *70*86*10^{-6}$

$I_{0}=0.68A$

(b)

when potential is at peak value then current will be zero

$I=0A$

(c)

V(t) = Vosin (27 ft)

$V(0)/2=V_{0}sin(2\pi ft)$

$1/2=sin(2\pi ft)$

$\pi /6=(2\pi ft)$

$t=1/12f$

so

$I(t)=\frac{V_{0}}{1/wC}sin(2\pi ft+\pi /2)$

$I(t)=\frac{V_{0}}{1/wC}sin(2\pi f*1/12f+\pi /2)$

$I(t)=\frac{V_{0}}{1/wC}sin(\pi /6+\pi /2)$

$I(t)=0.68sin(120^{0})$

$I(t)=0.59A$

(d)

V(t) = Vosin (27 ft)

$V(t)=18sin(2\pi *70*5*10^{-3})$

$V(t)=18sin(0.7\pi )$

$V(t)=18sin(126^{0})$

$V=14.56V$

and

$I(t)=-0.4A$

so power is

$P(t)=I(t)*V(t)$

$P(t)=0.4*14.56$

$P(t)=5.8W$