Question
Download Solution PDFA capacitor of capacitance C farad is connected in parallel with a resistance of R Ω. An AC voltage of V volt supplied across the circuit. if the current flowing through resistance is equal to IR and current flowing through the capacitors is equal to IC, What is the value of the total current flowing through the circuit?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFParallel RC circuit
In a resistor, the current is in the same phase as the voltage.
In a capacitor, the current leads voltage by 90°
Hence, for a parallel RC circuit, the angle of current (I) with respect to voltage (V) is between 0° to 90°
\(I_R={V\over R}\angle0\)
\(I_C={V\over 1/j\omega C}={j\omega CV}\)
\(I_C=\angle90 \space ({\omega CV})\)
The supply current is:
I = IR + j IC
\(I = {V\over R}+j\omega CV\)
\(\rm I=V\left(\frac{1}{R}+\omega C<90^{\circ}\right)\)
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