Answer to Question #173380 in Electric Circuits for Sandra

Question

In a PARALLEL circuit, the potential difference across each resistor is *

1 point

inversely proportional to its resistance

directly proportional to its resistance

directly proportional to the square of its resistance

unrelated to its resistance

Answer 1

In a parallel circuit, the voltage across each of the components is the same and the total current is the sum of the currents flowing through each component:

$$V=V_1=V_2,$$ $$I=I_1+I_2.$$

Applying Ohm's Law, we get:

$$I=\dfrac{V_1}{R_1}+\dfrac{V_2}{R_2}=\dfrac{V}{R_1}+\dfrac{V}{R_2},$$ $$I=V(\dfrac{1}{R_1}+\dfrac{1}{R_2})=\dfrac{V}{R_{eq}}.$$

Therefore, in a parallel circuit, the potential difference across each resistor is inversely proportional to its resistance.

Answer:

inversely proportional to its resistance