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GATE 2016 EE – Question 27

Electric Circuits · Network solution methods: KCL, KVL, Node and Mesh analysis · 1 mark · Numerical answer

In the portion of a circuit shown, if the heat generated in $5\ \Omega$ resistance is 10 calories per second, then heat generated by the $4\ \Omega$ resistance, in calories per second, is ________.

A $5\ \Omega$ resistor is connected in parallel with a series combination of a $4\ \Omega$ and a $6\ \Omega$ resistor.

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Correct answer: 1.9 to 2.1

Explanation

The heat rate in a resistor is $I^2 R$. In the 5 Ω resistor, $I_5^2 \times 5 = 10$, so $I_5^2 = 2$. The 5 Ω resistor and the series pair (4 Ω + 6 Ω = 10 Ω) share the same voltage, so the current in the series pair is $\frac{5 I_5}{10} = \frac{I_5}{2}$. The heat in the 4 Ω resistor is $\left(\frac{I_5}{2}\right)^2 \times 4 = I_5^2 = 2$ calories per second.