Physics

Physics

Problem

The current in the primary coil of a transformer is Ip=10sin⁡(100πt) AI_p = 10\sin(100\pi t)\,\text{A} (tt in seconds). If the mutual inductance between the coils is 0.20 H0.20\,\text{H}, calculate the instantaneous emf induced in the secondary coil at t=0.01 st = 0.01\,\text{s}. a) +314 V+314\,\text{V} b) +628 V+628\,\text{V} c) −628 V-628\,\text{V} d) +200 V+200\,\text{V}
Intuitive explanation

Mutual inductance tells you how strongly one coil's changing current influences the other—the induced emf in the secondary depends on how fast the primary current is changing, not the current itself. You'll need to differentiate the primary current to find dIpdt\frac{dI_p}{dt}, then apply Faraday's law for mutual inductance: εs=−MdIpdt\varepsilon_s = -M\frac{dI_p}{dt}. Finally, evaluate this expression at the given time.

Intuitive explanation

Mutual inductance tells you how strongly one coil's changing current influences the other—the induced emf in the secondary depends on how fast the primary current is changing, not the current itself. You'll need to differentiate the primary current to find dIpdt\frac{dI_p}{dt}, then apply Faraday's law for mutual inductance: εs=−MdIpdt\varepsilon_s = -M\frac{dI_p}{dt}. Finally, evaluate this expression at the given time.

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