A fixed amplitude V0 and AC voltage source of variable angular frequency are joined in series with capacitance C and an electric bulb of resistance R (inductance zero). When variable angular frequency is increased

As per the given values, When Variable Angular Frequency ω is increased, the following can occur:

The amplitudes of the voltages, in an AC circuit, across the components and the current are treated as vectors. Simply, the phase difference between voltage and current is apparently the angle between the vectors.

Now, assume the amplitude of the flowing current in the circuit = i

Therefore, magnitude of voltage vector of given resistance, V_R= i_R … [1]

\(\therefore\) Because voltage across resistance and current always are in phase, thereby the vectors of the voltage of resistance (V_R) and current (i) are found to be parallel.

Capacitance, in an AC circuit, serves as resistance to the circuit’s flow, also called the reactance of the circuit (Xc).

Thus,

Value of capacitive reactance equals, X_C= 1/ω_C … [2]

Here,

ω = Angular Frequency of the Source
C = Capacitance

Therefore, magnitude of the given voltage vector of capacitance equals, V_C= iX_C… [3]

A phase difference of −π/2 between the capacitor voltage and the current is found. The capacitor voltage lags the current behind by a phase of π/2. Thus, the vector of capacitor voltage (Vc) is found at an angle of −π/2 from the current vector.

Therefore, the resultant or the net voltage in the circuit is equal to, V_net = V_R+ V_C.

Note: “VR and VC are vectors and hence, Vnet is also a vector.”

Therefore, the magnitude of net voltage equals, V_net = √V²R + V²C

Now, after value substitution of VR and VC from equations [1] and [3].

⇒ V_net = √(iR)²+ (iXC)²

⇒ V_net=i√R²+ 1/ω²C²

Here, V_net= V0

⇒ I = V0/√R²+ 1ω²C²

Considering the value of ω is increased, the value of the current [1] will also increase. Now, the dissipated power via the resistance is expressed as P = i²R. Thus, the power in the given circuit will also rise. Now, if the power of the bulbs increases, it is more likely to glow brighter.

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1.
The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

2.
Assertion (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.

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If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

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Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

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A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be:

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If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

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A fixed amplitude V0 and AC voltage source of variable angular frequency are joined in series with capacitance C and an electric bulb of resistance R (inductance zero). When variable angular frequency is increased:

Related Questions

CBSE CLASS XII Related Questions

1.The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

2.Assertion (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.

3. If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

4.Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

5.A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be:

6. If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

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Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

2.
Assertion (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.

3.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

4.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

5.
A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be:

6.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.