Chapter 4

Resistors are manufactured so that their resistance lies within a tolerance band. Calculate the maximum and minimum values of the resistances given by: (a) \(10 \Omega \pm 3 \%\) (b) \(29 \mathrm{k} \Omega \pm 5 \%\) (c) \(3 \mathrm{M} \Omega \pm 0.1 \%\)

A steel track measures \(25 \mathrm{~m}\) at \(20^{\circ} \mathrm{C}\). At \(70{ }^{\circ} \mathrm{C}\) it measures \(25.01 \mathrm{~m}\). Calculate the percentage change in the length of the track as its temperature changes from \(20^{\circ} \mathrm{C}\) to \(70{ }^{\circ} \mathrm{C}\).

Brass is a mixture of copper and zinc in the ratio 8:3. Calculate the weight of zinc in \(20 \mathrm{~kg}\) of brass.

Divide 315 in the ratio \(6: 7: 8\).

The volume of gas in a cylinder is \(1098 \mathrm{~cm}^{3}\). Pressure is increased and the volume changes to \(936 \mathrm{~cm}^{3}\). Calculate the percentage change in the volume of gas.

A mass of \(176 \mathrm{~kg}\) is divided in the ratio 4:5:7. Calculate the mass of each portion.

A metal alloy is made from copper, zinc and steel in the ratio 3:4:1. (a) Calculate the amount of copper in a \(30 \mathrm{~kg}\) block of the alloy. (b) \(10 \mathrm{~kg}\) of copper is added to an existing \(40 \mathrm{~kg}\) block of the alloy to form a new alloy. Calculate the ratio of copper, zinc and steel in the new alloy.

Express the ratio \(1 \frac{1}{2}: 3 \frac{1}{4}\) using only integers.

Transmission lines have a nominal power rating of 30000 watts. If there are transmission losses of \(9 \%\) calculate the actual power transmitted.

The temperature of a chemical is reduced by \(6 \%\) to \(130{ }^{\circ} \mathrm{C}\). Calculate the original temperature to 2 d.p.