Physics

Problem

The V–I graphs for two resistors P and Q are straight lines through the origin. The line for P makes an angle of

30^{\circ}

with the current axis (I-axis), while that for Q makes an angle of

60^{\circ}

with the same axis. Determine the ratio of their resistances

R_{P} : R_{Q}

Intuitive explanation

The key is recognizing that resistance appears as the slope of a V–I graph: $R = V/I$ . Since both lines pass through the origin, the angle each line makes with the I-axis directly determines that slope—a steeper angle means a larger resistance. Use trigonometry to find each slope, then compare them to get the ratio.

Intuitive explanation

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