2.3-2.6 - Power, energy and mains electricity

Heating in resistors

A resistor is a component that makes it harder for charge to flow. When a current passes through a resistor, electrical energy is transferred in the resistor and the resistor's temperature increases.

One useful way to picture this is that the moving charges (electrons, in a metal) repeatedly collide with the atoms in the resistor and transfer energy to them. Energy is transferred to the resistor's internal energy store, so the atoms vibrate more and the temperature rises. In exam answers, keep the chain of reasoning clear:

current in resistor -> electrical energy transferred -> temperature increases

This heating effect is not always unwanted. It is deliberately used in domestic appliances where a heating element acts as a resistor. Examples include a kettle heating water, a toaster heating bread, an iron heating its base, and an electric heater warming the air nearby.

The same idea also explains why too large a current can be dangerous: wires and components have resistance, so a very large current can cause excessive heating. A fuse uses this effect on purpose: its thin wire heats up and melts when the current is too large, which breaks the circuit.

Power, current and voltage

The power of an appliance tells you how quickly it transfers energy. A high-power heater transfers energy faster than a low-power heater when both are working normally.

Power is measured in watts. One watt is one joule of energy transferred per second, so a $60\,\mathrm{W}$ lamp transfers $60\,\mathrm{J}$ of energy every second.

In this equation:

• $P$ is power in watts, $\mathrm{W}$
• $I$ is current in amperes, $\mathrm{A}$
• $V$ is voltage in volts, $V$

The equation can be rearranged depending on what the question asks for:

Worked example: a 24 W lamp is connected to a 12 V supply.

So the current in the lamp is $2.0\,\mathrm{A}$.

A common mistake is to treat watts as if they are the same thing as amperes. They are not. A watt is a unit of power; an ampere is a unit of current. The equation connects them only when the voltage is known.

Choosing fuses

A fuse is chosen from the normal current used by the appliance. In calculation questions, the usual route is:

1. Use the appliance power and supply voltage to calculate the normal operating current.
2. Choose a fuse rating just above that current from the ratings given.

For school calculation questions, choose the smallest supplied rating above the normal operating current. A fuse rating is not an exact current at which it instantly melts; operation depends on how large the excess current is and how long it lasts. It should not be much higher than necessary, because with a very high fuse rating a fault current that is unsafe for that appliance may flow without the fuse melting, so the cable or appliance could overheat.

Worked example: a $805\,\mathrm{W}$ appliance is connected to a $230\,\mathrm{V}$ mains supply. The available fuse ratings are $3\,\mathrm{A}$, $5\,\mathrm{A}$ and $13\,\mathrm{A}$.

The normal current is $3.5\,\mathrm{A}$, which exceeds the $3\,\mathrm{A}$ rating. Choose $5\,\mathrm{A}$: it is the smallest available rating above the normal current. The $13\,\mathrm{A}$ fuse permits a much larger current before operating.

If a question gives a calculated current of $2.6\,\mathrm{A}$ with available fuse ratings $1\,\mathrm{A}$, $3\,\mathrm{A}$ and $13\,\mathrm{A}$, choose $3\,\mathrm{A}$: it is above the normal current and is the smallest suitable rating.

Energy transferred over time

Power tells you the rate of energy transfer. If the same appliance is left on for longer, it transfers more energy. For this lesson, the required relationship combines current, voltage and time directly. It follows from power: $I \times V$ is the energy transferred each second, so multiplying it by the time in seconds gives the total energy transferred.

In this equation:

• $E$ is energy transferred in joules, $\mathrm{J}$
• $I$ is current in amperes, $\mathrm{A}$
• $V$ is voltage in volts, $V$
• $t$ is time in seconds, $\mathrm{s}$

Use seconds for time unless the question clearly tells you to use another unit. If a time is given in minutes, convert it first: for example, $5\ \text{minutes} = 5 \times 60 = 300\,\mathrm{s}$.

Worked example: a $2.0\,\mathrm{A}$ heater is connected to a $230\,\mathrm{V}$ supply for $60\,\mathrm{s}$.

So $27600\,\mathrm{J}$ of energy is transferred.

The equation can be rearranged in the same way as $P = I \times V$. For example, to find a time, use $t = E / (I \times V)$.

Notice the direct proportionality: if current and voltage stay the same, doubling the time doubles the energy transferred. That is why leaving an appliance on for longer transfers more energy.

A.c. and d.c.

Mains electricity is alternating current, written a.c.. In an alternating current, the current repeatedly changes direction. In the UK, the mains supply is about $230\,\mathrm{V}$ and has a frequency of $50\,\mathrm{Hz}$: it goes through 50 complete cycles every second.

A cell or battery supplies direct current, written d.c.. In a direct current, the current flows in one direction only.

[DIAGRAM: asset_name: Power, energy and mains electricity - diagram 01; asset_slug: p14_power_energy_and_mains_electricity__diagram_01; recommended_method: matplotlib; description: NovaLearn pale-palette two-panel current-time graphs with time axes at zero: steady positive d.c. from a cell or battery and two sinusoidal a.c. mains cycles crossing zero into opposite current directions.]

On both graphs, the horizontal time axis marks zero current. The d.c. line stays at the same value above it: the current is steady and in one direction. The a.c. curve rises above the zero line and then falls below it: below the line, the current is flowing in the opposite direction.

The d.c. line shown is steady, but direct current can vary in size while staying in one direction. The sign of the a.c. graph shows its direction: crossing zero and changing sign means reversal.

The key distinctions are:

• mains electricity is a.c.
• a cell or battery supplies d.c.
• a.c. changes direction repeatedly
• d.c. flows in one direction only

Do not say that a.c. means the current is sometimes on and sometimes off. The current reverses direction; it is still supplying energy to the appliance during normal operation.

Quick recap

• Current through a resistor transfers energy to its internal energy store; this heating is useful in appliances but excessive current can overheat wiring.
• Electrical power is $P=IV$. Calculate normal current with $I=P/V$, then choose the smallest supplied fuse rating above it in school problems.
• Electrical energy is $E=IVt$; use seconds to obtain joules when current is in amperes and voltage in volts.
• Mains a.c. repeatedly reverses direction. Cell or battery d.c. flows in one direction, even if its magnitude changes.