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Alternating Current — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsAlternating Current1 Mark
MCQ
In an alternating current circuit consisting of elements in series, the current increases on increasing the frequency of supply. Which of the following elements are likely to constitute the circuit?
  • A
    Only resistor.
  • B
    Resistor and an inductor.
  • C
    Resistor and a capacitor.
  • D
    Only a capacitor.
✓

Answer

  1. Resistor and a capacitor.
  2. Only a capacitor.

Solution:

This is the similar problem as we discussed above. In this problem, the current increases on increasing the frequency of supply. Hence, the reactance of the circuit must be decreased as increase in frequency. So, one element that must be connected is capacitor. We can also connect a resistor in series.

For a capacitive circuit,

$\text{X}_\text{C}=\frac{1}{\omega\text{C}}=\frac{1}{2\pi\text{fC}}$

When frequency increases, XC decreases. Hence current in the circuit increases.

Importance point: Resistive, Capacitive Circuit (RC-Circuit)

VR = iR,

VC = iXC,

VR = iR

  1. Applied voltage: $\text{V}=\sqrt{\text{V}^2_\text{R}+\text{V}^2_\text{C}}$

  2. Impedance: $\text{Z}=\sqrt{\text{R}^2+\text{X}^2_\text{C}}=\sqrt{\text{R}^2+\Big(\frac{1}{\omega\text{C}}\Big)^2}$

  3. Current: $\text{i}=\text{i}_0\sin(\omega\text{t}+\phi)$

  4. Peak current: $\text{i}_0=\frac{\text{V}_0}{\text{Z}}=\frac{\text{V}_0}{\sqrt{\text{R}^2+\text{X}^2_\text{C}}}=\frac{\text{V}_0}{\sqrt{\text{R}^2+\frac{1}{4\pi^2\text{v}^2\text{C}^2}}}$

  5. Phase difference: $\phi=\tan^{-1}\frac{\text{X}_\text{C}}{\text{R}}=\tan^{-1}\frac{1}{\omega\text{CR}}$

  6. Power factor: $\cos\phi=\frac{\text{R}}{\sqrt{\text{R}^2+\text{X}^2_\text{C}}}$

  7. Leading quantity: Current.

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