How do you find the resistance of a parallel circuit

Asked by admin @ 28/10/2021 in Physics viewed by 280 People

How do you think the total resistance of a parallel circuit is calculated?

Answered by admin @ 28/10/2021

Let's consider two resistors only for simplicity. When the resistors are connected in parallel, the potential difference on each resistor is the same, and it is equal to the voltage of the battery, V:
$V_1 = V_2 = V$ (1)
Instead, the current splits in the two resistors:
$I=I_1 + I_2$ (2)
where I is the current in the circuit, I1 and I2 are the currents in the two resistors.
By using Ohm's law, we can rewrite (2) as
$\frac{V}{R_{eq}} = \frac{V_1}{R_1}+ \frac{V_2}{R_2}$ (3)
where $R_{eq}$ is the equivalent resistance of the circuit. But we also said that
$V_1 = V_2 = V$
So we can rewrite (3) as
$\frac{V}{R_{eq}}= \frac{V}{R_1}+ \frac{V}{R_2}$
which becomes
$\frac{1}{R_{eq}}= \frac{1}{R_1}+ \frac{1}{R_2}$

So, the equivalent resistance of the parallel of n resistors is given by
$\frac{1}{R_{eq}}= \frac{1}{R_1}+ \frac{1}{R_2}+...+ \frac{1}{R_n}$

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