Four resistors of 5 - 10 - 15 - and 20 - are connected in parallel- Calculate the total resistance of the circuit-

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Kirchoff's Voltage Law

Four resistor...

Question

Four resistors of $5 Ω$ , $10 Ω$ , $15 Ω$ and $20 Ω$ 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 $R_{1} = 5 Ω$
The resistance of the second resistor $R_{2} = 10 Ω$
The resistance of the third resistor $R_{3} = 15 Ω$
The resistance of the third resistor $R_{3} = 20 Ω$
The formula for the total resistance $R_{p}$ for the parallel combination is
$\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}}$
Step 2 - Finding the total resistance of the circuit
Substitute the values into the above formula and solve to calculate $R_{p}$ .
$\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}} \frac{1}{R_{p}} = \frac{1}{(5 Ω)} + \frac{1}{(10 Ω)} + \frac{1}{(15 Ω)} + \frac{1}{(20 Ω)} \frac{1}{R_{p}} = \frac{12 + 6 + 4 + 3}{60} \frac{1}{R_{p}} = \frac{25}{60} R_{p} = \frac{60}{25} R_{p} = 2.4 Ω$
Hence, the total resistance of the circuit is $2.4 Ω$ .

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