The table shows the resistivity, length and cross-sectional area of wires P and Q - AQA - A-Level Physics - Question 27 - 2017 - Paper 1

The resistance of wire Q is calculated as:

$R_Q = \frac{\frac{\rho}{4} \, L}{A} = \frac{R}{4}$

For two resistors in parallel, the total resistance ($R_T$) is given by:

$\frac{1}{R_T} = \frac{1}{R_P} + \frac{1}{R_Q}$

Substituting the values of $R_P$ and $R_Q$:

$\frac{1}{R_T} = \frac{1}{R} + \frac{4}{R}$

This simplifies to:

$\frac{1}{R_T} = \frac{5}{R}$

Thus, the total resistance is:

$R_T = \frac{R}{5}$