CAIE IGCSE Physics 4.3.2.10 Combined resistance of two resistors

Practise calculating the combined resistance of two parallel resistors, including mixed circuits and unknown resistor values.

Exam points

use 1/R = 1/R1 + 1/R2 or R1R2/(R1+R2) for two parallel resistors
work backwards from total resistance to find an unknown parallel resistor
combine a parallel pair first, then add any series resistance in the circuit

[Maximum number: 2]

A cylindrical metal wire $\mathrm{W}_{1}$ , of length l and cross-sectional area A, has a resistance of $16 \Omega$ . A second cylindrical wire $\mathrm{W}_{2}$ having length $\frac{l}{2}$ and cross-sectional area 2 A, is made from the same metal.

Determine

the effective resistance of $\mathrm{W}_{1}$ and $\mathrm{W}_{2}$ when connected in parallel.

resistance of parallel pair =

$1 \div \mathrm{R}=\left(1 \div \mathrm{R}_{1}\right)+\left(1 \div \mathrm{R}_{2}\right)$ OR $\mathrm{R}=\left(\mathrm{R}_{1} \times \mathrm{R}_{2}\right) \div\left(\mathrm{R}_{1}+\mathrm{R}_{2}\right)$ OR $(1 \div \mathrm{R})=(1 \div 4)+(1 \div 16)$ OR $(4 \times 16) \div(4+16)$ $3.2 \Omega$

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4.3.2.10—Combined resistance of two resistors question 1