Day: July 24, 2023

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202307241011 Solution to 2023-DSE-PHY-IA-25

Two cells of negligible internal resistance are connected to two resistors as shown.

Roughwork.

Label the nodes a, b, c, and d:

Identify potential differences \Delta V_{ab}, \Delta V_{cd}, \Delta V_{ac}, and \Delta V_{bd}:

Lemma. (Kirchhoff’s 2nd law (/voltage law/loop rule))

The directed sum of the potential differences (voltages) around any closed loop is zero.

Wikipedia on Kirchhoff’s circuit laws

\begin{aligned} \Delta V_{ab}+\Delta V_{bd}+\Delta V_{dc}+\Delta V_{ca} & = 0 \\ (3)+((-I)(1))+(-(1.5))+(-(I)(2)) & = 0 \\ I & = +0.5\,\mathrm{A} \\ \end{aligned}

This problem is not to be attempted.