Question

​​​A 318uf capacitor is connected across a 230V, 50Hz supply, determine.

i. The capacitive reactance, 

ii. The r.m.s value of current ​

iii. Equations for voltage and current

Answer 1

v = 230 v

f = 50 HZ

c = 318 x 10^-6

(i) The capacitive reactance

\(X_c=\frac{1}{wc}\)

\(X_c=\frac{1}{2\pi fc}\)

\(X_c=\frac{1}{2\pi\times50\times318\times10^{-6}}\)

\(X_c=\frac{1}{2\times3.14\times50\times318\times10^{-6}}\)

X_c = 10.01 Ω

(ii) The rms value of current 

\(i_{rms}=\frac{V_{rms}}{X_c}⇒\frac{230}{10.01}\) = 22.97 ampere

(iii) Equation of current

I = I_o Sin(ωt +π/2)

I = 22.97 sin(100πt +π/2)

v = v₀ sin (ωt)

v = 230 sin (100πt)