Question

Two capacitors, a 20 mF and a 30 mF, are connected in parallel to a 400 Hz source. The total capacitive reactance is _____.

Answer 1

Answer-

The total capacitive reactance of the circuit is 7.96 Ω.

Solution-

Two capacitors, a 20 mF and a 30 mF, are connected in parallel to a 400 Hz source.

The effective/equivalent capacitance of the circuit is,

$C=20+30=50\ mF$

As, when capacitors are connected together in parallel, the equivalent capacitance in the circuit is equal to the sum of capacitance of all the individual capacitor.

We know that,

$X_c=\dfrac{1}{2\pi fC}$

Where,

$X_c$ = Capacitive Reactance (in Ω)

f = frequency (in Hz)

C = Capacitance (in F)

Here given,

$X_c$ = ??

f = 400 Hz

C = 50 mF = $50\times 10^{-6}$ F

Putting the values in the formula,

$X_c=\dfrac{1}{2\pi \times 400\times 50\times 10^{-6}}$

$X_c=\dfrac{10^{6}}{40000\pi}$

$X_c=7.96\ \Omega$

Therefore, the total capacitive reactance of the circuit is 7.96 Ω.