Physics

Problem

The circuit described here contains two batteries and three resistors forming two loops with one resistor common to both. Parameters:

R_1 = 8\,\Omega

R_2 = 10\,\Omega

R_3 = 4\,\Omega

\mathcal E_1 = 20\,\text{V}

(positive terminal at top of left loop), and

\mathcal E_2 = 16\,\text{V}

(positive terminal at bottom of right loop). The lower ends of the two batteries are connected together, and the upper ends of

R_1

and

R_2

are joined by

R_3

as in earlier questions. (a) Choose suitable loop current directions and calculate the numerical values of those currents. (b) Determine the power supplied by each battery (give sign convention clearly). (c) Determine the power dissipated in each resistor. (d) Verify, by numerical comparison, that the algebraic sum of powers supplied and powers dissipated in the entire circuit is zero.

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