A 60μF capacitor is connected to a 110V, 60Hz ac supply. Determine the rms value of the current in the circuit.
Exercise
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Capacitance of capacitor, $\text{C}=60\mu\text{F}=60\times10^{-6}\text{F}$
Supply voltage, V = 110V
Angular frequency, $\omega=2\pi\text{V}$
Capacitive reactance $\text{X}_{\text{c}}=\frac{1}{\omega\text{C}}$
$=\frac{1}{2\pi\text{vC}}$
$=\frac{1}{2\times3.14\times60\times60\times10^{-6}}\Omega^{-1}$
Rms value of current is given as:
$\text{I}=\frac{\text{v}}{\text{X}_{\text{c}}}$
$= 110 \times 2 \times 3.14 \times 60 \times 10^{-6} \times 60 = 2.49A$
Hence, therms value of current is 2.49A.
Supply voltage, V = 110V
Angular frequency, $\omega=2\pi\text{V}$
Capacitive reactance $\text{X}_{\text{c}}=\frac{1}{\omega\text{C}}$
$=\frac{1}{2\pi\text{vC}}$
$=\frac{1}{2\times3.14\times60\times60\times10^{-6}}\Omega^{-1}$
Rms value of current is given as:
$\text{I}=\frac{\text{v}}{\text{X}_{\text{c}}}$
$= 110 \times 2 \times 3.14 \times 60 \times 10^{-6} \times 60 = 2.49A$
Hence, therms value of current is 2.49A.
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