Question 24 of 31intermediate🔧 ApplyNumerical3 marks

Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of (i) 9 Ω, (ii) 4 Ω.

(i)

so that the combination has a resistance of 9 Ω

Answer

To get 9 Ω: Connect two resistors in parallel, then connect this combination in series with the third resistor. Parallel combination: 1/R = 1/6 + 1/6 = 2/6 = 1/3, so R = 3 Ω. Series combination: Total R = 3 + 6 = 9 Ω.

(ii)

so that the combination has a resistance of 4 Ω

Answer

To get 4 Ω: Connect two resistors in series, then connect this combination in parallel with the third resistor. Series combination: R = 6 + 6 = 12 Ω. Parallel combination: 1/R = 1/12 + 1/6 = 1/12 + 2/12 = 3/12 = 1/4, so R = 4 Ω.

Explanation

This question tests understanding of series and parallel resistor combinations. For series, resistances add directly (R_s = R_1 + R_2 + R_3). For parallel, reciprocals add (1/R_p = 1/R_1 + 1/R_2 + 1/R_3). By combining these two methods, students can achieve intermediate resistance values that neither pure series nor pure parallel can provide alone.

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