Question

Three resistors, A, B, and C, are connected in parallel and attached to a battery, with the resistance of A being the smallest and the resistance of C the greatest. Which resistor carries the highest current?

Answer 1

Answer:

Resistor A

Explanation:

Resistors A, B and C are connected in parallel to a battery of voltage represented by V.

Since they are in parallel, the same voltage, V, passes across the three of them.

And from Ohm's law, the voltage (V) through a resistor is the product of the current (I) flowing through it and the resistance (R) of the resistor. i.e

V = I x R

=> I = $\frac{V}{R}$

Therefore, assuming the values of the resistances of resistors A, B and C are A, B and C respectively,

(i) the current, $I_{A}$ through A is

$I_{A}$ = $\frac{V}{A}$

(ii) the current, $I_{B}$ through B is

$I_{B}$ = $\frac{V}{B}$

(iii) the current, $I_{C}$ through C is

$I_{C}$ = $\frac{V}{C}$

From the foregoing, it can be deduced that the current is inversely proportional to the resistance. Therefore, the higher the resistance, the lower the current. Consequential of this, the resistor that carries the highest current is the one with the smallest resistance, which is A