An R-C circuit is driven by an alternating voltage of amplitude 110 V and frequency w. Define V0 to be amplitude of the voltage across the resistor. The resistance of the resistor is 1000 ohms and the capacitance of the capacitor is 1 microFarad. What is V0 if w=10 rad/s? Any help you could give on how this is worked out would be appreciated. Thanks.

Question

An R-C circuit is driven by an alternating voltage of amplitude 110 V and frequency w.  Define V0 to be amplitude of the voltage across the resistor.  The resistance of the resistor is 1000 ohms and the capacitance of the capacitor is 1 microFarad.  What is V0 if w=10 rad/s?  Any help you could give on how this is worked out would be appreciated. Thanks.

bobpursley · Answer

find impedance: Z= 1000-.159j/wC figure that impedance, magnitude then Vo=IR=110^2/Z * R so you know Z magnitude, and R, solve for Vo

Henry · Answer

Xc = 1/WC = 1/(10*1*10^-6) = = 1*10^5 Ohms. Z = R-jXc = 1000 - j100,000 = 100,005 Ohms[-89.4o] I = E/Z = 110/100,005 = 0.0011A Vo = I*R = 0.0011 * 1000 = 1.1 Volts.