The four resistors 5Ω, 15Ω 3Ω and 30Ω are connected in parallel and connected to the circuit. What is the equivalent resistance of this resistor connection?

1.58Ω

Explanation:

R1 = 5Ω

R2 = 15Ω

R3 = 3Ω

R4 = 30Ω

The equivalent resistance of the resistor connection (Rtotal) of the four resistors connected in parallel is obtained by adding the reciprocal of each resistance.

i.e 1/Rtotal = (1/R1 + 1/R2 + 1/R3 +1/R4)

1/Rtotal = (1/5Ω + 1/15Ω + 1/3Ω + 1/30Ω)

Make 30Ω the lowest common multiple

1/Rtotal = (6 + 2 + 10 + 1)/30Ω

1/Rtotal = 19/30Ω

To get the value of Rtotal, cross multiply

1 x 30Ω = Rtotal x 19

30Ω = Rtotal x 19

Rtotal = 30Ω/19

Rtotal = 1.58Ω

Thus, the equivalent resistance of this resistor connection is 1.58Ω

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