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Physics

You are given three resistors of magnitude 3 Ω each. You can join them either in a series or in a parallel combination. How will you arrange them so that the equivalent resistance would become:

(a) maximum

(b) minimum

(Your answer must be accompanied by proper mathematical calculations)

Current Electricity

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Answer

Given,
Number of resistors = 3
Resistance of each resistor, R = 3 Ω

(a) To get maximum equivalent resistance: Connect all in series combination, resistances simply add:

Rs=R+R+R=3+3+3=9Ω\text{R}_{\text s} = \text{R} + \text{R} + \text{R} = 3 + 3 + 3 = 9 Ω

This is the maximum possible equivalent resistance using all three.

(b) To get minimum equivalent resistance: connect all in parallel combination.

By the reciprocal formula:

1Rp=1R+1R+1R1Rp=13+13+131Rp=33Rp=33=1Ω\dfrac{1}{R{\text p}} = \dfrac{1}{R} + \dfrac{1}{R} + \dfrac{1}{R} \\[1em] \dfrac{1}{R{\text p}}= \dfrac{1}{3} + \dfrac{1}{3} + \dfrac{1}{3} \\[1em] \dfrac{1}{R{\text p}}= \dfrac{3}{3} \\[1em] \\[1em] R{\text p} = \dfrac{3}{3} = 1 Ω

This gives the minimum possible equivalent resistance.

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