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Question 11 Mark

A current $\text{i}_1=\text{i}_0\sin\omega\text{t}$ passes through a resistor of resistance R. How much thermal energy is produced in one time period? A current $\text{i}_2=-\text{i}_0\sin\omega\text{t}$ passes through the resistor. How much thermal energy is produced in one time period? If i₁, and i₂ both pass through the resistor simultaneously, how much thermal energy is produced? Is the principle of superposition obeyed in this case?

Answer

$\text{I}_\text{rms}^{2}\times\text{R}\times\frac{2\pi}{\omega}$ from definition of rms current.

i₁, and i₂ both pass through the resistor simultaneously, and same thermal energy is produced.

Similary, the principle of superposition obeyed in this case zero.

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Question 21 Mark

An AC source is connected to a capacitor. Will the rms current increase, decrease or remain constant if a dielectric slab is inserted into the capacitor?

Answer

$\text{X}_\text{c}=\frac{1}{\omega\text{C}}$ as slab is introduced C increases and X_C decreases so current increases.

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Question 31 Mark

Can a hot-wire ammeter be used to measure a direct current having a constant value? Do we have to change the graduations?

Answer

Yes, in this case I_rms value will be same as the DC current.

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Question 41 Mark

In a circuit containing a capacitor and an AC source the current is zero at the. stant the source voltage is maximum. Is it consistent with Ohm's law?

Answer

Ohm's law is valid for resistance.

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Question 51 Mark

Can the peak voltage across the inductor be greater than the peak voltage of the source in an LCR circuit?

Answer

Yes,
Consider example below:

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Question 61 Mark

When an AC source is connected to a capacitor there is a steady-state current in the circuit. Does it mean thatthe charges jump from one plate to the other to complete the circuit?

Answer

No.

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Question 71 Mark

Is energy produced when a transformer steps up the voltage?

Answer

No, as voltage increases current decreases. Hence, if efficiency is 100% power will be same.

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Question 81 Mark

When the frequency of the AC source in an LCR circuit equals the resonant frequency, the reactance of the circuit is zero. Does it mean that there is no current through the inductor or the capacitor?

Answer

There is current but the potential difference across inductor and capacitor cancel each other.

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Question 91 Mark

Two alternating currents are given by, $\text{i}_\text{i}=\text{i}_0\sin\omega\text{t}$ and $\text{i}_\text{i}=\text{i}_0\sin\Big(\omega\text{t}+\frac{\pi}{3}\Big)$ Will the rms values of the currents be equal or different?

Answer

I_rms will be equal because in a complete cycle heat dissipated will be equal for both.

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Question 101 Mark

Can you, have an AG series circuit in which there is. a phase difference of 180° between the emf and the current? 120°?

Answer

No.

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Question 111 Mark

What is the reactance of a capacitor connected to a constant DC source?

Answer

$\text{X}_\text{c}=\frac{1}{\omega\text{C}}$

As,

$\omega=0$

For,

$\text{DC},\text{X}_\text{c}=\infty.$

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