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Alternating Current question

2024 · 9 Apr · Shift 1 · Q79
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Alternating Current question

2024 · 9 Apr · Shift 1 · Q79

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :
  1. A
    becomes zero
  2. B
    remains same
  3. C
    increases
  4. D
    decreases
View written solutionFree

Correct answer: C

  1. Series circuit in AC

A bulb behaves approximately like a resistor RRR, and the capacitor has capacitive reactance

XC=1ωCX_C = \frac{1}{\omega C}XC​=ωC1​

So the total impedance of the series circuit is

Z=R2+XC2Z = \sqrt{R^2 + X_C^2}Z=R2+XC2​​

and the current is

I=VZ=VR2+XC2I = \frac{V}{Z} = \frac{V}{\sqrt{R^2 + X_C^2}}I=ZV​=R2+XC2​​V​

  1. Effect of inserting a dielectric

When a dielectric is placed between the plates of the capacitor, its capacitance increases:

C′=KC(K>1)C' = K C \quad (K>1)C′=KC(K>1)

Therefore the capacitive reactance decreases:

XC′=1ωC′=1ωKC=XCKX_C' = \frac{1}{\omega C'} = \frac{1}{\omega K C} = \frac{X_C}{K}XC′​=ωC′1​=ωKC1​=KXC​​

So,

XC′<XCX_C' < X_CXC′​<XC​

  1. Effect on total impedance and current

Since XCX_CXC​ decreases, the total impedance becomes

Z′=R2+XC′2Z' = \sqrt{R^2 + {X_C'}^2}Z′=R2+XC′​2​

which is smaller than before:

Z′<ZZ' < ZZ′<Z

Hence the current increases:

I′=VZ′>VZ=II' = \frac{V}{Z'} > \frac{V}{Z} = II′=Z′V​>ZV​=I

  1. Glow of the bulb

The brightness of the bulb depends on the power dissipated in it:

P=I2RP = I^2 RP=I2R

Since RRR is unchanged and III increases, the power increases. Therefore the bulb glows more brightly.

  1. Option check
  • A: becomes zero — false
  • B: remains same — false
  • C: increases — true
  • D: decreases — false

Therefore, the correct answer is:

C: increases\boxed{\text{C: increases}}C: increases​

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