Question

draw a circuit diagram to show three resistors connected in parallel with a cell and key . write the formula for the equivalent resistor R of this combination if the individual resistance of the resistor R1, R2 and R3.

Answer 1

Answer:

The formula for the equivalent resistor R of this combination is $R=\dfrac{R_{1}R_{2}R_{3}}{R_{2}R_{3}+R_{3}R_{1}+R_{1}R_{2}}$.

Explanation:

Given that,

First resistance =R₁

Second resistance =R₂

Third resistance = R₃

According to figure,

Three resistors connected in parallel with a cell and key.

The equivalent resistor R will be

$\dfrac{1}{R}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}$

$R=\dfrac{R_{1}R_{2}R_{3}}{R_{2}R_{3}+R_{3}R_{1}+R_{1}R_{2}}$

Hence, The formula for the equivalent resistor R of this combination is $R=\dfrac{R_{1}R_{2}R_{3}}{R_{2}R_{3}+R_{3}R_{1}+R_{1}R_{2}}$.