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A voltage waveform V(t) = 12t2 is applied across 1 H inductor for t ≥ 0, with initial current through it being zero. The current through inductor for t ≥ 0 will be-
- a)4t3
- b)12t3
- c)24 t
- d)12 t
Correct answer is option 'A'. Can you explain this answer?
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A voltage waveform V(t) = 12t2is applied across 1 H inductor for t &ge...
Given that, V(t) = 12t2
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A voltage waveform V(t) = 12t2is applied across 1 H inductor for t &ge...
The current through the inductor can be found using the formula:
V = L di/dt
where V is the voltage across the inductor, L is the inductance, and di/dt is the rate of change of the current.
In this case, we have V(t) = 12t^2 and L = 1 H. Differentiating V(t) with respect to time, we get:
dV/dt = 24t
Substituting these values into the formula, we get:
12t^2 = 1 di/dt
di/dt = 12t^2
Integrating both sides with respect to time, we get:
i(t) = 4t^3 + C
where C is the constant of integration. To find C, we use the initial condition that the current through the inductor is zero when t = 0:
i(0) = 0 = 4(0)^3 + C
C = 0
Therefore, the current through the inductor is:
i(t) = 4t^3
The graph of the current versus time is a cubic function that starts at zero and increases rapidly with time.
V = L di/dt
where V is the voltage across the inductor, L is the inductance, and di/dt is the rate of change of the current.
In this case, we have V(t) = 12t^2 and L = 1 H. Differentiating V(t) with respect to time, we get:
dV/dt = 24t
Substituting these values into the formula, we get:
12t^2 = 1 di/dt
di/dt = 12t^2
Integrating both sides with respect to time, we get:
i(t) = 4t^3 + C
where C is the constant of integration. To find C, we use the initial condition that the current through the inductor is zero when t = 0:
i(0) = 0 = 4(0)^3 + C
C = 0
Therefore, the current through the inductor is:
i(t) = 4t^3
The graph of the current versus time is a cubic function that starts at zero and increases rapidly with time.
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A voltage waveform V(t) = 12t2is applied across 1 H inductor for t ≥ 0, with initial current through it being zero. The current through inductor for t ≥ 0 will be-a)4t3b)12t3c)24 td)12 tCorrect answer is option 'A'. Can you explain this answer?
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