Exercise 13.4
Worked answers to exercise 13.4.
Question 1 — where each is used
Direct current
Torches, calculators, mobile phones and laptops, from their batteries
A car's electrical system and its starter motor
Electroplating and charging batteries
Alternating current
The mains supply to homes, 230 V
The national grid, through transformers
A bicycle dynamo lighting its lamp
Question 2 — which kind of current
Each graph shows current against time. The question is only whether the current ever changes direction — that is, whether the graph crosses to the other side of zero.
| t | 0 | 0.3 | 0.5 | 0.8 | 1.3 | 1.8 | 2 | 2.2 | 2.4 | 2.7 | 2.9 | 3.1 | 3.3 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | 0.35 | 0.5 | 0.4 | 0.2 | 0.45 | 0.75 | 0.5 | 0.65 | 0.5 | 0.8 | 0.45 | 0.6 | 0.5 |
(a) Direct: the current varies but stays positive.
| t | 0 | 0.05 | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 | 0.35 | 0.4 | 0.45 | 0.5 | 0.55 | 0.6 | 0.65 | 0.7 | 0.75 | 0.8 | 0.85 | 0.9 | 0.95 | 1 | 1.05 | 1.1 | 1.15 | 1.2 | 1.25 | 1.3 | 1.35 | 1.4 | 1.45 | 1.5 | 1.55 | 1.6 | 1.65 | 1.7 | 1.75 | 1.8 | 1.85 | 1.9 | 1.95 | 2 | 2.05 | 2.1 | 2.15 | 2.2 | 2.25 | 2.3 | 2.35 | 2.4 | 2.45 | 2.5 | 2.55 | 2.6 | 2.65 | 2.7 | 2.75 | 2.8 | 2.85 | 2.9 | 2.95 | 3 | 3.05 | 3.1 | 3.15 | 3.2 | 3.25 | 3.3 | 3.35 | 3.4 | 3.45 | 3.5 | 3.55 | 3.6 | 3.65 | 3.7 | 3.75 | 3.8 | 3.85 | 3.9 | 3.95 | 4 | 4.05 | 4.1 | 4.15 | 4.2 | 4.25 | 4.3 | 4.35 | 4.4 | 4.45 | 4.5 | 4.55 | 4.6 | 4.65 | 4.7 | 4.75 | 4.8 | 4.85 | 4.9 | 4.95 | 5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | 0 | 0.13 | 0.25 | 0.36 | 0.47 | 0.57 | 0.65 | 0.71 | 0.76 | 0.79 | 0.8 | 0.79 | 0.76 | 0.71 | 0.65 | 0.57 | 0.47 | 0.36 | 0.25 | 0.13 | 0 | 0.13 | 0.25 | 0.36 | 0.47 | 0.57 | 0.65 | 0.71 | 0.76 | 0.79 | 0.8 | 0.79 | 0.76 | 0.71 | 0.65 | 0.57 | 0.47 | 0.36 | 0.25 | 0.13 | 0 | 0.13 | 0.25 | 0.36 | 0.47 | 0.57 | 0.65 | 0.71 | 0.76 | 0.79 | 0.8 | 0.79 | 0.76 | 0.71 | 0.65 | 0.57 | 0.47 | 0.36 | 0.25 | 0.13 | 0 | 0.13 | 0.25 | 0.36 | 0.47 | 0.57 | 0.65 | 0.71 | 0.76 | 0.79 | 0.8 | 0.79 | 0.76 | 0.71 | 0.65 | 0.57 | 0.47 | 0.36 | 0.25 | 0.13 | 0 | 0.13 | 0.25 | 0.36 | 0.47 | 0.57 | 0.65 | 0.71 | 0.76 | 0.79 | 0.8 | 0.79 | 0.76 | 0.71 | 0.65 | 0.57 | 0.47 | 0.36 | 0.25 | 0.13 | 0 |
(b) Direct: it rises and falls to zero, but never goes negative (a full-wave rectified current).
| t | 0 | 0.4 | 0.8 | 1.1 | 1.5 | 1.7 | 1.8 | 2.2 | 2.4 | 2.5 | 2.7 | 3.3 | 3.5 | 3.6 | 3.75 | 3.85 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | 0 | 0.8 | 0.05 | -0.7 | 0.05 | 0.1 | 0.05 | 0.6 | 0.7 | 0.8 | 0.95 | -0.1 | -0.55 | -0.05 | -0.15 | 0 |
(c) Alternating: it goes both positive and negative.
| t | 0 | 0.2 | 0.5 | 0.8 | 1 | 1.2 | 1.4 | 1.7 | 2 | 2.3 | 2.5 | 2.8 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | -0.4 | -0.35 | -0.8 | -0.4 | -0.5 | -0.4 | -0.45 | -0.3 | -0.5 | -0.4 | -0.5 | -0.45 |
(d) Direct: it varies but stays negative, so it always flows the same (reverse) way.
| t | 0 | 0.5 | 0.5 | 1 | 1 | 1.5 | 1.5 | 2 | 2 | 2.5 | 2.5 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | 0.8 | 0.8 | -0.8 | -0.8 | 0.8 | 0.8 | -0.8 | -0.8 | 0.8 | 0.8 | -0.8 | -0.8 |
(e) Alternating: a square wave that jumps between positive and negative.
| t | 0 | 0.4 | 0.4 | 0.6 | 0.6 | 1 | 1 | 1.2 | 1.2 | 1.6 | 1.6 | 1.8 | 1.8 | 2.2 | 2.2 | 2.6 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | -0.8 | -0.8 | 0 | 0 | -0.8 | -0.8 | 0 | 0 | -0.8 | -0.8 | 0 | 0 | -0.8 | -0.8 | 0 | 0 |
(f) Direct: pulses that switch on and off but always on the negative side.
Why (b) is not alternating
Graph (b) looks like the AC of a dynamo, and it came from one — but a rectifier, like the bridge of chapter 11, has flipped every negative half up. The current now rises and falls to zero, yet always flows the same way, so it is direct. The same test sorts all six: find zero on the current axis and ask whether the line ever crosses to the other side.
Below the axis is still direct
A graph drawn wholly below zero, like (d) and (f), is a direct current flowing the other way. Only a graph that crosses zero, like (c) and (e), is alternating.