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Question

An RLC circuit is driven by a sinusoidal emf with angular frequency ω. If the angular frequency is increased without changing the amplitude of the emf, the current amplitude increases, it means?


A

ωL>1ωC

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B

ωL<1ωC

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C

ωL=1ωC

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D

None of the options

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Solution

The correct option is C

ωL=1ωC


Step 1: Given data

It is given that the angular frequency is increased without changing the amplitude of the emf and the current amplitude increases.

Step 2: Formula used

E=IZ

Where E is emf, I is current and Z is the impedance of the circuit.

Z=R2+XL-XC2Z=R2+Lω-1Cω2

Where R is resistance, XL is the inductive reactance, XC is the capacitive reactance, L is the inductance, C is the capacitance and ω is the angular frequency.

Step 3: Calculation

We know in an RLC circuit, E=IZ where E is emf, I is current and Z is the impedance of the circuit.

Here, as it is given that the amplitude of emf is constant, the current is inversely proportional to the impedance of the circuit.

I1Z

It means as current increases Z must decrease. Since impedance,

Z=R2+XL-XC2Z=R2+Lω-1Cω2

Z will decrease if R=0 or Lω-1Cω=0.

As R cannot be zero,

ωL-1ωC=0ωL=1ωC

The solution is ωL=1ωC

hence, option C is correct.


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