Q. 44.0( 26 Votes )

# A 60 μF capacitor is connected to a 110 V, 60 Hz A.C. supply. Determine the rms value of the current in the circuit.

Answer :

Given: capacitance = 60 μF = 60 × 10^{-6} F

Voltage V = 110 V

Frequency f = 60 Hz

The diagram is:

Capacitive reactance is given by the following relation:

X_{c} = 1/ωC

Substituting ω = 2πv in the above formula, we get

X_{c} = 1/2πvC

Substituting the values, we get

⇒

Now, the root mean square value of the current can be calculated as follows:

I_{rms} = V/X_{c}

I_{rms} = 110V × 2 × 3.14 × (60Hz) × 60 × 10^{-6}(F)

On calculating, we get

I_{rms} = 2.49 A

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Figure shows a typical circuit for low-pass filter. An AC input V_{i} = 10 mV is applied at the left end and the output V0 is received at the right end. Find the output voltages for v = 10 kHz, 100 k Hz, 1.0 MHz and 10.0 MHz Note that as the frequency is increased the output decreases and hence the name low-pass filter.

HC Verma - Concepts of Physics Part 2