Physics Alternating Current

A 750 Hz, 20 V (rms) source is connected to a resistance of 100Ω, an inductance of 0.1803H and a capacitance of 10µF all in series. The time in which the resistance (heat capacity 2 J/°C) will get heated by 10°C. (assume no loss of heat to the surroundings) is close to:

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Contributor-Level 10

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For the given input voltage waveform Vin(t), the output voltage waveform Vo(t), across the capacitor is correctly depicted by:

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Contributor-Level 10

τ = RC = 10µS
For 0

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An AC circuit has R = 100Ω, C = 2µF and L = 80mH, connected in series. The quality factor of the circuit is:

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Contributor-Level 10

Q = (1/R)√ (L/C) = (1/100)√ (80e-3/2e-6) = 2

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A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant ' $b$ ', the connect equivalence would be:

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Contributor-Level 10

In damped oscillation

$∴ v_{2} = \frac{1}{8} * \frac{1}{T} = \frac{1}{8} * \frac{10^{16}}{1.6} = 7.8 * 10^{14}$

$m a + b v + k x = 0$

In the circuit

$m \frac{d^{2} x}{{d t^{2}}^{2}} + b \frac{d x}{d t} + k x = 0$

$- i R - L \frac{d i}{d t} - \frac{q}{C} = 0$

Comparing equation (i) and (ii)

$L \frac{d^{2} q}{d t^{2}} + R \frac{d q}{d t} + \frac{1}{c} q = 0$

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An emf of $20 V$ is applied at time $t = 0$ to a circuit containing in series $10 m H$ inductor and $5 Ω$ resistor. The ratio of the currents at time $t = \infty$ and at $t = 40 s$ is close to: (take $e^{2} = 7.389)$

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$\begin{array}{r} i & = \frac{V}{r} (1 - e^{- R t / L}) \\ = 4 (1 - e^{- 500 t}) \end{array}$

At $t = \infty$

$i_{1} = 4 A$

at $t = 40 s$

$i_{2} = 4 (1 - e^{- 20000})$

$= 4 [1 - \frac{1}{{(e^{2})}^{10000}}]$

$= 4 [1 - \frac{1}{(7.389)^{10000}}]$

$\frac{i_{1}}{i_{2}}$ is slightly greater than 1 .

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A sinusoidal voltage of peak value 250V is applied to a series LCR circuit, in which R = 8â„¦, L = 24mH andC = 60Î¼F. The value of power dissipated at resonant condition is â€˜xâ€™ kW. The value of x to the nearest integer is-----------.

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Raj Pandey

Contributor-Level 9

Kindly consider the following Image

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For the given circuit, comment on the type of transformer used.

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Contributor-Level 10

Voltage across secondary source
P = V? i? = V? i?
V? = P/i? = 60/0.11 ≈ 545 V
Since voltage across secondary source is more than primary source (220V)
⇒ Step- up transformer.

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For the circuit shown, the value of current at time t = 3.2 s will be _____ A.

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A 100Ω resistance, a 0.1 µF capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

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Contributor-Level 10

ω = 2πf = 1/√ (LC)
L = 1/ (4π²f²C) = 1/ (4π² * 60² * 0.1*10? ) = 70.3 mH

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Two circuits are shown in the figure (a) & (b). At a frequency of __________ rad /s the average power dissipated in one cycle will be same in both the circuits.

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