Question

An AC source operating at 60 Hz with a maximum voltage of 173 V is connected in series with a resistor (R = 1.3 k?) and a capacitor (C = 2.5

Answer 1

a)

Capacitive reactance

X_c=1/2pifC =1/2pi*60*(2.5*10^-6) =1061.03 ohms

Impedance

Z=sqrt[R²+X_c²]=sqrt[1300²+1061.03²]=1678.03 ohms

maximum current

I_max=V_max/Z =173/1678.03

I_max=0.103 A

b)

V_R,max=I_max*R =0.103*1300 =134 Volts

V_c,max=I_max*X_c=0.103*1061.03 =109.3 Volts

c)

When Current is zero ,the instantaneous voltage across resistor is

V_R=I*R=0 Volts

Instantaneous Voltage across capacitor is

V_c=V_max =109.3 Volts

Instantaneous voltage around the circuit is

V_source=V_R+V_c=109.3 Volts

charge on the capacitor at that instant

Q=CV =(2.5)*109.3=273.25 uC

d)

When the current is at a maximum ,the instantaneous voltage across resistor is

V_R=I*R=134 Volts

Instantaneous Voltage across capacitor is

V_c=0 Volts

Instantaneous voltage around the circuit is

V_source=V_R+V_c=134 Volts

charge on the capacitor at that instant

Q=CV =0 uC