The total resistance of three parallel resistors is

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Solution

Step1: Resistance in parallel
:
Ammeter reading when connected in a series to the circuit
$I = I_{1} + I_{2} + I_{3}$
voltmeter reading will be constant in the circuit
$V = I R$
Step2: Solving
$I_{1} = \frac{V}{R_{1}}$
$I_{2} = \frac{V}{R_{2}}$
$I_{3} = \frac{V}{R_{3}}$
on adding the above three equations
$I_{1} + I_{2} + I_{3} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}}$
$I_{1} + I_{2} + I_{3} = V (\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}})$
$\frac{I}{V} = (\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}})$
and the equivalent resistance is R_T
$R_{T} = \frac{V}{I}$
hence,
$\frac{1}{R_{T}} = (\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}})$
The total resistance of three parallel resistors is $\frac{1}{R_{T}} = (\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}})$ .

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