(a) What is the maximum value of the current inthe circuit? Enter anumber. 1 A (
ID: 1721909 • Letter: #
Question
(a) What is the maximum value of the current inthe circuit?Enter anumber. 1 A
(b) What are the maximum values of the potential difference acrossthe resistor and the capacitor?
VR, max = Enter anumber. 2 V
VC, max = Enter anumber. 3 V
(c) When the current is zero, what are the magnitudes of thepotential difference across the resistor, the capacitor, and the ACsource?
vR = Enter an exactnumber. 4 V
vC = Enter anumber. 5 V
vsource = Enter anumber. 6 V
How much charge is on the capacitor at this instant?
qc = Enter anumber. 7 µC
(d) When the current is at a maximum, what are the magnitudes ofthe potential differences across the resistor, the capacitor, andthe AC source?
vR = Enter anumber. 8 V
vC = Enter an exactnumber. 9 V
vsource = Enter anumber. 10 V
How much charge is on the capacitor at this instant?
qc = Enter an exactnumber. 11 µC Enter anumber. Enter anumber. Enter anumber. Enter an exactnumber. Enter anumber. Enter anumber. Enter anumber. Enter anumber. Enter an exactnumber. Enter anumber. Enter an exactnumber.
Explanation / Answer
we are given with
f = 60 Hz
Vmax = 170 V
R = 1.2 k
= 1.2 x 103
C = 2.5 C
= 2.5 x 10-6 C
the capacitive reactance is given by
XC = 1 / 2 f C
= ........
the impedence Z is given by
Z = [R2 + (XL -XC)2]
as XL = 0
Z = [R2 +(XC)2]
= .........
(a)
the maximum current will be
Imax = Vmax / Z
=........ A
(b)
the maximum values of the potential difference acrossthe resistor will be
VRmax = Imax R
= ........ V
the maximum values of the potential difference acrossthe capacitor will be
VCmax = ImaxXC
= ........ V
(c)
when the instantaneous current i is zero theinstantaneous voltage across the resistor is
vR = i R
= 0
the instantaneous voltage across the capacitor isalways 90o or a quarter cycle out of phase with
the instantaneous current
so we get
when i = 0
vC = VCmax
= ........ V
charge is
qC = C vC
= ......... C
the kirchoffs rule always applies to the instantaneousvoltage around a closed loop
for the series circuit
vsource = vR + vC
vsource = 0 + VCmax
= ....... V
(d)
when the instantaneous current is maximum that is i =Imax the instantaneous voltage across the
resistor will be
vR = i R
= ImaxR
= VRmax
= .......... V
the instantaneous voltage across the capacitor isa quarter cycle out of phase with the current so
when i = Imax we must get
vC = 0
qC = C vC
= 0
now applying the kirchoofs loop rule to theinstantaneous voltage around the series circuit at the
instant when i = Imax gives
vsource = vR + vC
= VRmax + 0
= ......... V
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