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Consider a series RL circuit in which current 12 A is flowing through R and current 16 A is flowing through L. The current supplied by the sinusoidal current source I is ____________
- a)28 A
- b)4 A
- c)20 A
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
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Consider a series RL circuit in which current 12 A is flowing through ...
Current I (t) is given by,
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Consider a series RL circuit in which current 12 A is flowing through ...
Given:
- Current through resistor R = 12 A
- Current through inductor L = 16 A
We need to find the current supplied by the sinusoidal current source.
To find the current supplied by the sinusoidal current source, we can use the concept of phasors. A phasor is a complex number that represents the magnitude and phase of a sinusoidal quantity.
Let's assume that the sinusoidal current source has a phasor value of I0∠θ, where I0 is the magnitude and θ is the phase angle.
The phasor representation of the current through the resistor R is I_R = 12∠0°.
The phasor representation of the current through the inductor L is I_L = 16∠90°.
Since the resistor and inductor are connected in series, the current through them must be the same. Therefore, we can equate the phasor values of the current through the resistor and inductor.
I_R = I_L
12∠0° = 16∠90°
To equate the magnitudes, we can divide both sides of the equation by 4.
3∠0° = 4∠90°
Now, we can see that the magnitude of the sinusoidal current source is 4 A (I0 = 4) and the phase angle is 0° (θ = 0°).
Therefore, the current supplied by the sinusoidal current source is 4 A.
Hence, the correct answer is option b) 4 A.
- Current through resistor R = 12 A
- Current through inductor L = 16 A
We need to find the current supplied by the sinusoidal current source.
To find the current supplied by the sinusoidal current source, we can use the concept of phasors. A phasor is a complex number that represents the magnitude and phase of a sinusoidal quantity.
Let's assume that the sinusoidal current source has a phasor value of I0∠θ, where I0 is the magnitude and θ is the phase angle.
The phasor representation of the current through the resistor R is I_R = 12∠0°.
The phasor representation of the current through the inductor L is I_L = 16∠90°.
Since the resistor and inductor are connected in series, the current through them must be the same. Therefore, we can equate the phasor values of the current through the resistor and inductor.
I_R = I_L
12∠0° = 16∠90°
To equate the magnitudes, we can divide both sides of the equation by 4.
3∠0° = 4∠90°
Now, we can see that the magnitude of the sinusoidal current source is 4 A (I0 = 4) and the phase angle is 0° (θ = 0°).
Therefore, the current supplied by the sinusoidal current source is 4 A.
Hence, the correct answer is option b) 4 A.
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