Optimizing a Circuit

Electricity and Magnetism Level 3

The DC circuit above consists of two voltage sources \(V_1\) and \(V_2\) with internal resistances \(R_1 = 1 \Omega\) and \(R_2 = 2 \Omega\) respectively. There is a load \(R_L = 3 \Omega\) connected in parallel with the sources.

\(V_1\) and \(V_2\) are variable quantities.

Let \(P_1\), \(P_2\), and \(P_L\) be the amounts of power in watts dissipated by \(R_1\), \(R_2\), and \(R_L\) respectively.

Given that \(P_L = 10\) watts, determine the minimum possible value of \(P_1 + P_2 + P_L\) to 1 decimal place.

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