A combination consists of three resistors in series. Four similar sets are connected in parallel. If the resistance of each resistor is 2Ω. Find the equivalent resistance of the combination.

Foundation

Physics Foundation

Ohms Law and Resistance

Question

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Concept used :

· Series Resistance :

R_series = R₁ + R₂ +....+ R_n

· Parallel Resistance :

\frac{1}{R_{parallel}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \dots + \frac{1}{R_{n}}

Step 1 : ldentify the knowns and unknowns

· Resistance of one resistor R = 2Ω

· Three such resistors are in series to make one set.

· Four such sets are in parallel.

· The equivalent resistance of the combination Req = ?

Step : Determine the total resistance of one set

Three resistors of R = 2Ω each are in series to make one set.

R_set = R + R + R = 3R

⇒ R_set = 3 × 2Ω = 6Ω,

Step 3 : Determine the total resistance of 4 such sets in parallel

Four resistors of R_set = 6Ω each are in parallel to make one combination.

\frac{1}{R_{eq}} = \frac{1}{R_{set}} + \frac{1}{R_{set}} + \frac{1}{R_{set}} + \frac{1}{R_{set}} = \frac{4}{R_{set}}

\Rightarrow \frac{1}{R_{eq}} = \frac{4}{6 Ω}

\Rightarrow R_{eq} = \frac{6}{4} Ω

⇒ R_eq = 1.5Ω

Answer :

The equivalent resistance of the combination is R_eq = 1.5Ω

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