GATE EC 2025 Set 1 — Question 65
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Electromagnetics → Circuit Fundamentals & Theorems → Differential & Integral Forms
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Question
Two resistors are connected in a circuit loop of area , as shown in the figure below. The circuit loop is placed on the x-y plane. When a time-varying magnetic flux, with flux-density (in Tesla), is applied along the positive z-axis, the magnitude of current (in Amperes, rounded off to two decimal places) in the loop is _________.
Correct answer
0.62 to 0.63
Solution
Given:
Area of the circuit loop .
The loop is placed on the x-y plane, so the area vector is in the z-direction.
Magnetic flux density along the positive z-axis. So, .The magnetic flux through the loop is given by:
According to Faraday's Law of Induction, the induced electromotive force (EMF) is:
The magnitude of the induced EMF is .From the figure, the two resistors are connected in series in the loop. Each resistor has a value of .
Total resistance of the loop .The magnitude of the current flowing in the loop is given by Ohm's Law:
Rounded off to two decimal places, the magnitude of the current is .
Area of the circuit loop .
The loop is placed on the x-y plane, so the area vector is in the z-direction.
Magnetic flux density along the positive z-axis. So, .The magnetic flux through the loop is given by:
According to Faraday's Law of Induction, the induced electromotive force (EMF) is:
The magnitude of the induced EMF is .From the figure, the two resistors are connected in series in the loop. Each resistor has a value of .
Total resistance of the loop .The magnitude of the current flowing in the loop is given by Ohm's Law:
Rounded off to two decimal places, the magnitude of the current is .
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