Question

A series RC circuit consists of resistor with a resistance of 50 Ω and a capacitor of capacitance of 

c)Derive an equation of the instantaneous voltage across the capacitor, 𝑉𝐶.

 𝑉𝑅= 10.5 cos2000𝜋𝑡

e)Determine the equation of the instantaneous voltage of the ac source, 𝑣𝑠

a)Derive an equation for the instantaneous current that flows in the circuit.

20 µF.The instantaneous voltage across the resistor 𝑉𝑅is given as;

.

b)Calculate the reactance of the circuit.

d)Sketch a phasor diagram of the circuit.

Answer 1

a)

$I= \frac{V_R}{R}\\ I= \frac{10.5 cos (2000 \pi t)}{50}\\ I=0.2cos (2000 \pi t)$

b)

$=\frac{1}{j wC}\\ =\frac{1}{j 2000 \pi*22*10^{-6}}\\ =-j 7.234 Ω$

c)

$V_C= I*X_C\\ V_C= \frac{10.5 cos 2000 \pi t}{50}* \frac{1}{j 2000 \pi*22*10^{-6}}=1.45 sin(2000 \pi t)\\$

d)

e)

$V_s= V_R+V_C\\ =10.5 \angle 0^0+1.45 \angle -90^0\\ =10.1 \angle cos (2000 \pi t-8.2)$