Question

When a potential difference of 10 V is placed across a certain solid cylindrical resistor, the current through it is 3 A. If the diameter of this resistor is now tripled, the current will be: A) 2/9 A B) 2/3 A C) 27 A D) 18 A.

Answer 1

Answer:

C) 27 A

Explanation:

ΔV = Potential difference across the cylindrical resistor = 10 V

i = current through the resistor = 3 A

R = Resistance of the resistor

Using ohm's law

ΔV = i R

10 = 3 R

R = 3.33 ohm

The resistance of a resistor is inversely related to square of the diameter. So as the diameter is tripled, the resistance becomes 1/9 times

R' = New resistance of the resistor  = $\frac{R}{9}$

i' = new current through the resistor

Using ohm's law

ΔV = i' R'

$10 = i'\frac{R}{9}$

$10 = i'\frac{3.33}{9}$

i' = 27 A