Question

Two cylindrical resistors are made from same material and have the same length. When connected across the same battery, one dissipates twice as much power as the other. How do their diameters compare ?

Answer 1

Answer:

$\frac{d_2}{d_1} = \sqrt2 = 1.41$

Explanation:

As resistor is connected to the battery of constant EMF then the power across the resistor is given as

$P = \frac{E^2}{R}$

now if two resistors are made up of same material and of same length then due to different cross sectional area they both have different resistance

Due to different resistance they both will have different power

Since power is inversely depends on the resistance

So if the power is twice that of the other then the resistance must be half

so we have

$R_1 = \rho \frac{L}{A_1}$

$R_2 = \rho\frac{L}{A_2}$

since one resistance is half that of other resistance

So the area of one must be twice that of other

so we have

$\frac{A_2}{A_1} = 2$

$\frac{\pi d_2^2}{\pi d_1^2} = 2$

$d_2 = 1.41 d_1$