GRE Physics GR1777 Problem 004 Solution

GRE Physics GR 1777 Problem Solution

004. Electrodynamics


Net resistance in a parallel circuit is
$latex \\frac{1}{R_{parallel}} = \\frac{1}{R_1} + \\frac{1}{R_2} = \\frac{1}{1} + \\frac{1}{2} = \\frac{3}{2}$

$latex \\therefore R_{parallel} = \\frac{2}{3}$

Then, total resistance in circuit is
$latex R_{total} = 1 + \\frac{2}{3} = \\frac{5}{3}$.

By the Ohm\’s law, $latex V = IR$, the total current is $latex 20 = \\frac{5}{3} \\cdot I$,
$latex \\therefore I = 12A$.

In a parallel circuit, the current is divided. The ratio of the individual current is the inverse ratio as individual resistance, so
$latex R{1} : R{2} = 1 : 2 = 1/I{1} : 1/I{2}$.

Therefore, the current $latex i$ through the $latex 2\\Omega$ resistor is 4A.



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