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Make a rule: how would you find the resistance of a parallel circuit with

Make a rule: how would you find the resistance of a parallel circuit with n identical resistors?

2 months ago

Solution 1

Guest Guest #4093
2 months ago
When n resistors are connected in parallel, it means they are connected to the same potential difference V:
V=V_1 =V_2 =...=V_n (2)
It also means that the total current in the circuit is given by the sum of the currents flowing through each branch (each resistor) of the circuit:
I=I_1+I_2 +...+I_n (1)

By using Ohm's law:
I= \frac{V}{R}
we can rewrite (1) as
\frac{V}{R_{eq}} = \frac{V_1}{R_1}+ \frac{V_2}{R_2}+...+ \frac{V_n}{R_n}
However, we said that the potential difference across each resistor is equal (eq.(2)), so we can rewrite the last formula as
\frac{V}{R_{eq}} = \frac{V}{R_1}+ \frac{V}{R_2}+...+ \frac{V}{R_n}
From which we find an expression for the equivalent resistance of n resistors in parallel:
\frac{1}{R_{eq}}= \frac{1}{R_1}+ \frac{1}{R_2}+....+ \frac{1}{R_n}

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