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Alternating Current

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4 months ago

Alternating Current Class 12th

As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is $\frac{\sqrt[]{a}}{π} A .$ The value of a is __________.

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alok kumar singh

Contributor-Level 10

Let l = l₀ cos wt

Then v = v₀ sinwt

at t = 0, v = 0

but l = l₀

$l_{r m s} = \frac{l_{0}}{\sqrt[]{2}}$

$V_{r m s} = l_{r m s} z$

$\Rightarrow 220 = \frac{l_{0}}{\sqrt[]{2}} (X_{L})$

$\Rightarrow 220 = \frac{l_{0}}{\sqrt[]{2}} (2 π * 50 * 200 * 1 0^{- 3})$

$\Rightarrow 220 = \frac{l_{0}}{\sqrt[]{2}} (20 π)$

$l_{0} = \frac{220 \sqrt[]{2}}{20 π}$

$l_{0} = \frac{11 \sqrt[]{2}}{π} = \frac{\sqrt[]{a}}{π}$

a = 121 * 2

a = 242

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4 months ago

Alternating Current Class 12th

At t < 0, the capacitor is charged and the switch is opened. At t = 0 the switch is closed. The shortest time T at which the charge on the capacitor will be zero is given by:

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alok kumar singh

Contributor-Level 10

The time period of LC oscillations,

$T = 2 π \sqrt[]{L C}$

The time at which charge on the capacitor will be zero is $\frac{T}{4} .$

So t $= \frac{π}{2} \sqrt[]{L C}$

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4 months ago

Alternating Current Class 12th

A resonance circuit having inductance and resistance 2 * 10^-4 H and 6.28 $Ω$ respectively oscillates at 10 MHz frequency. The value of quality factor of this resonator is__________.

[p = 3.14]

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alok kumar singh

Contributor-Level 10

Quality factor = $\frac{ω L}{R} = \frac{2 * 3.14 * 10 * 1 0^{6} * 2 * 1 0^{- 4}}{6.28} = 2000$

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4 months ago

Alternating Current Class 12th

A series LCR circuit containing 5.0H inductor, 80μF capacitor and 40Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:

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alok kumar singh

Contributor-Level 10

Q = ω? L/R ⇒ Δω = R/L = 50/4 = 8rad/sec
Δω
ω? = 1/√LC = 1/√ (5*80*10? ) = 50rad/sec
ω? = ω? - Δω/2 = 46rad/sec
ω? = ω? + Δω/2 = 54rad/sec

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4 months ago

Alternating Current Class 12th

A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?

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alok kumar singh

Contributor-Level 10

220 * i? = 44
⇒ I? = 44/220 = 1/5 = 0.2 A

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4 months ago

Alternating Current Class 12th

An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance ' R '
are connected in series to an ac source of potential difference ' V volts as shown in figure.
Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10√2 A. The impedance of the circuit is:

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alok kumar singh

Contributor-Level 10

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New answer posted

4 months ago

Alternating Current Class 12th

A screw gauge gives the following readings when used to measure the diameter of a wire
Main scale reading: 0 mm
Circular scale reading: 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is:

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alok kumar singh

Contributor-Level 10

Least count = 1 mm / 100 = 0.01 mm
Diameter = main scale reading + circular scale reading
Diameter = 0 + 52 * 0.01 mm
= 0.52 mm = 0.052 cm

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4 months ago

Alternating Current Class 12th

An ac source is connected to a capacitor $C$ . Due to decrease in its operating frequency:

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alok kumar singh

Contributor-Level 10

Speed of light in air is

$C = \frac{x}{t_{1}}$

Speed of light in another denser medium.

$C_{2} = \frac{10 x}{t_{2}}$

$\Rightarrow μ = \frac{C}{C_{2}} = \frac{x}{t_{1}} * \frac{t_{2}}{10 x}$

$\Rightarrow μ = \frac{t_{2}}{10 t_{1}}$

(d) $Δ θ = \frac{λ}{d}$

$Δ θ$ is proportional to $λ$ but independent of $D$ .

for minimum wavelength, maximum loss of energy

$e V = (\frac{h c}{λ})$

$λ \propto (\frac{1}{V})$

(b) Incident energy $= 2.20 e V$

If $? < 2.20 e V$ electron will emit.

$? > 2.20 e V$ No electron emission

Only caesium will emit electron

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4 months ago

Alternating Current Class 12th

A $12 V, 60 W$ lamp is connected to the secondary of a step down transformer, whose primary is connected to ac mains of $220 V$ . Assuming the transformer to be ideal, what is the current in the primary winding?

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alok kumar singh

Contributor-Level 10

$B = \frac{E}{C} = \frac{48}{3 * 10^{8}} = 16 * 10^{- 8}$

$= 1.6 * 10^{- 7} T$

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4 months ago

Alternating Current Class 12th

Match List-I with List-II

List - I	List - II
(a) Phase difference between current and voltage in a purely resistive AC circuit	(i) π/2; current leads voltage
(b) Phase difference between current and voltage in a pure inductive AC circuit	(ii) Zero
(c) Phase difference between current and voltage in a pure capacitive AC circuit	(iii) π/2; current lags voltage
(d) Phase difference between current and voltage in an LCR series circuit	(iv) tan?¹((X_L - X_C)/R)

Choose the most appropriate answer from the options given below :

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alok kumar singh

Contributor-Level 10

In a purely resistive AC circuit, if V = V? sin (ωt), then the current I is:
I = (V? / X? ) * sin (ωt - π/2)

0 0

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