Can you explain the answer of this question below:An alternating e.m.f. of angular frequency ω is applied across an inductance. The instantaneous power developed in the circuit has an angular frequencyA:ω/4B:ω/2C:ωD:2ωThe answer is d.

Question

Answer

The instantaneous values of emf and current in inductive circuit are given by E=E0sinωt and i=i0sin(ωt−π2)respectively. So, Pinst=Ei=E0sinωt*i0sin(ωt−π2) =E0i0sinωt(sinωtcosπ2−cosωtsinπ2) =E0i0sinωt cosωt =12E0i0sin2ωt (sin2ωt=2sinωt cosωt) Hence, angular frequency of instantaneous power is 2ω.

Answer

Answer

Answer

Explanation:

The power developed in an inductor is given by the formula:

P = VI cos(θ)

Where,
P = Power developed in the circuit
V = Voltage across the inductor
I = Current flowing through the inductor
θ = Phase angle between voltage and current

In an inductor, the current lags behind the voltage by a phase angle of 90 degrees. This means that the power developed in an inductor is always zero because the cosine of 90 degrees is zero.

However, when an alternating e.m.f. is applied across an inductance, the current flowing through the inductor also becomes alternating. The current lags behind the voltage by a phase angle of 90 degrees, but the magnitude of the current changes with time.

Instantaneous Power:

The instantaneous power is given by the formula:

P(t) = VI cos(θ)

Where,
P(t) = Instantaneous power at time t
V = Voltage across the inductor
I = Instantaneous current flowing through the inductor
θ = Phase angle between voltage and current

Since the current is alternating, its magnitude changes with time. Therefore, the instantaneous power also changes with time.

Angular Frequency:

The angular frequency (ω) is the rate at which the alternating current changes its direction. It is given by the formula:

ω = 2πf

Where,
ω = Angular frequency
f = Frequency of the alternating current

Answer:

In this question, an alternating e.m.f. of angular frequency ω is applied across an inductance. This means that the current flowing through the inductor also has an angular frequency ω.

Since the instantaneous power is given by the formula P(t) = VI cos(θ), the angular frequency of the instantaneous power will be the same as the angular frequency of the current, which is ω.

Therefore, the correct answer is option D: ω. The angular frequency of the instantaneous power developed in the circuit is ω.

Answer

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