Three resistors of 2 - 3 - and 15 - are connected in parallel- Calculate the total resistance of the circuit-

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Kirchoff's Voltage Law

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Question

Three resistors of $2 Ω$ , $3 Ω$ and $15 Ω$ are connected in parallel. Calculate the total resistance of the circuit.

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Solution

Step 1 - Given data and formula
The resistance of the first resistor $R_{1} = 2 Ω$
The resistance of the second resistor $R_{2} = 3 Ω$
The resistance of the third resistor $R_{3} = 15 Ω$
The formula for the total resistance $R_{p}$ for the parallel combination is
$\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$
Step 2 - Finding the total resistance of the circuit
Substitute the values into the above formula and solve to calculate $R_{p}$ .
$\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} \frac{1}{R_{p}} = \frac{1}{(2 Ω)} + \frac{1}{(3 Ω)} + \frac{1}{(15 Ω)} \frac{1}{R_{p}} = \frac{15 + 10 + 2}{30} \frac{1}{R_{p}} = \frac{27}{30} R_{p} = \frac{30}{27} R_{p} = 1.11 Ω$
Hence, the total resistance of the circuit is $1.11 Ω$ .

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Three resistors of 2Ω, 3Ω and 15Ω are connected in parallel. Calculate the total resistance of the circuit.

Three resistors of $2 Ω$ , $3 Ω$ and $15 Ω$ are connected in parallel. Calculate the total resistance of the circuit.