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Solved Problems-5

A 20 Ω resistor is connected in series with an inductor, a capacitor and an ammeter across a 25 V variable frequency supply. When the frequency is 400 Hz, the current is at its maximum value of 0.5 A and the potential difference across the capacitor is 150 V. Calculate:
  1. The capacitance of the capacitor.
  2. The resistance and inductance of the inductor.
Here, R = 20 Ω, Vm = 25 Volt, f = 400 Hz, I = 0.5 A, VC = 150 Volt
When the current is the maximum, the circuit is in resonance and hence total reactances
XL ~ XC = 0
  1. The capacitance value is calculated as,
    ∴ Description: 3302.png
    ⇒ Description: 3308.png
  2.  XL ~ XC = 0
    ∴ XL = XC
    ⇒ Description: 3344.png
    ⇒ Description: 3353.png
Also, at resonance, circuit resistance = circuit impedance
Description: 1360.png
Let, r = resistance of the inductor
Then Description: 3359.png

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