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In the circuit given below, the KVL for first loop is ___________(a) V (t) = R1i1 + L1 \(\frac{di_1}{dt}\) + M \(\frac{di_2}{dt}\)(b) V (t) = R1i1 – L1 \(\frac{di_1}{dt}\) – M \(\frac{di_2}{dt}\)(c) V (t) = R1i1 + L1 \(\frac{di_1}{dt}\) – M \(\frac{di_2}{dt}\)(d) V (t) = R1i1 – L1 \(\frac{di_1}{dt}\) + M \(\frac{di_2}{dt}\)I have been asked this question in examination.My query is from Advanced Problems Involving Complex Circuit Diagram topic in chapter Network Theory and Complex Circuit Diagram of Network Theory

Answer»

Right answer is (C) V (t) = R1i1 + L1 \(\frac{di_1}{dt}\) – M \(\frac{di_2}{dt}\)

To explain: We know that, in general, the KVL is of the form V (t) = R1i1 + L1 \(\frac{di_1}{dt}\) + M \(\frac{di_2}{dt}\)

But here, M term is NEGATIVE because i1, is entering the dotted terminal and i2, is leaving the dotted terminal.

So, V (t) = R1i1 + L1 \(\frac{di_1}{dt}\) – M \(\frac{di_2}{dt}\).


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