Irodov Problem 3.191

The key insight is that current naturally divides between parallel resistors to minimize total power dissipation—this is a consequence of Kirchhoff's laws and energy conservation. Since $P = I^2R$, current preferentially flows through the lower-resistance path. You'll verify this by showing that if current were distributed differently (say, more through the higher resistor), the total power $P_{total} = I_1^2R_1 + I_2^2R_2$ would increase, confirming that the actual distribution is indeed the minimum.

The key insight is that current naturally divides between parallel resistors to minimize total power dissipation—this is a consequence of Kirchhoff's laws and energy conservation. Since $P = I^2R$, current preferentially flows through the lower-resistance path. You'll verify this by showing that if current were distributed differently (say, more through the higher resistor), the total power $P_{total} = I_1^2R_1 + I_2^2R_2$ would increase, confirming that the actual distribution is indeed the minimum.