GATE 2023 BM – Question 38

Electrical Circuits · Network Theorems · 2 marks · Multiple choice

In the shown circuit, the DC sources have voltages V₁ and V₂. To which expression is the power dissipated in the 60 kΩ resistor proportional?

$(V_1+V_2)^2$
$(3V_1+V_2)^2$
$(2V_1+V_2)^2$
$(V_1+2V_2)^2$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $(2V_1+V_2)^2$

Explanation

Let the central voltage be V. Kirchhoff’s current law gives (V−V₁)/10+(V−V₂)/20+V/60=0, with resistances in kilohms. Multiplying by sixty gives 10V=6V₁+3V₂, so V=(3/10)(2V₁+V₂). Power is V²/60 kΩ and is therefore proportional to (2V₁+V₂)², C.

More Network Theorems questions

GATE 2023 BM Q46 – In the shown 10 V circuit, what load resistance R gives maximum power dissipation in R?
GATE 2022 BM Q52 – Find the magnitude of current gain Iload/Iin in the shown dependent-source circuit, to two…
GATE 2021 BM Q13 – Three resistors are connected to ideal sources as shown: current source 1.2 A, voltage…
GATE 2021 BM Q39 – In the shown bridge, Vₛ=100 V, R₁=30 Ω,R₂=60 Ω,R₃=90 Ω,R₄=45 Ω,R₅=30 Ω. Find current…
GATE 2020 BM Q41 – Find the nearest power dissipated in the 3 Ω resistor of the shown circuit, with 2 A…
GATE 2026 BM Q29 – Find the Thevenin voltage in volts at the RLoad terminals of the shown 15 V, three-100 Ω…

All Network Theorems questions →