What Electricity Does in a Theatre

Four quantities, three formulae, and one habit: never describe a circuit without saying where you are measuring from.

Why a technical director needs this#

You will spend your career signing off other people's electrical work. Not doing it, most of the time: signing it off. A designer wants a practical lamp inside a period fitting. A production electrician tells you a dimmer will not run an LED fixture. A scenic automation supplier hands you a schematic with an emergency stop loop drawn on it, and asks you to confirm the circuit is acceptable.

In every one of those conversations you need to be able to do one thing: tell the difference between a claim that holds and a claim that sounds like it holds. That is what this course is for. Not to make you an electrician, and not to make you an electronic engineer. To make you someone who cannot be told a comfortable lie about electricity.

The whole subject reduces to a single sentence you should be able to say by the end of today:

Every effect in a live show is a controlled release of energy. Everything here is about controlling it deliberately, proving that you did, and knowing what happens when it fails.

What actually kills shows#

It is worth being honest about the failure modes, because they are not the dramatic ones.

Almost everything that goes wrong is mechanical, thermal or organisational. The physics is usually fine. That is why this course spends more hours at a bench than at a whiteboard.

The four quantities#

Everything in the first half of this course is four quantities and the relationships between them. Learn what each one does before you learn its formula, because the formula is trivial and the intuition is not.

Voltage is a difference, never a place#

Voltage is the difference in electrical pressure between two points. It is meaningless to say "this wire is at 12 volts" without saying relative to what. A bird on an 11 kV line is at 11 kV and is entirely comfortable, because both its feet are at the same potential.

This is not a pedantic point. It is the single most common source of confusion in fault-finding, and it is why every measurement you write down this term must record both probes.

Current is what does the work, and what does the damage#

Current is the rate of charge flow: how much is moving, per second. Voltage is what pushes; current is what actually heats a cable, lights a lamp, moves a motor, and stops a heart.

When you hear somebody say "it is only 12 volts, it is safe", they are half right and they do not know which half. Twelve volts across dry skin will not push meaningful current through you, so it is safe to touch. Twelve volts through a car battery can deliver four hundred amps into a spanner and weld it to the terminal. The voltage was never the dangerous part.

Resistance is opposition, and it is where the heat appears#

Resistance opposes current, and every ohm of it converts electrical energy into heat. That is not a side effect; that is the entire operating principle of a filament lamp, a heater, and a smouldering connector.

Anywhere current flows through unintended resistance, you get unintended heat. A loose terminal is a resistor you did not design. This is why "it works, but that connector is warm" is not a description of a working system.

Power is the rate of energy, and it is what you pay for and plan for#

Power is what the distribution board cares about, what the generator hire quote is priced on, and what determines whether a cable is comfortable or a fire.

The three formulae#

There are three, and you will use them for the rest of your career.

V = I × R          Ohm's law
P = V × I          Power
P = I² × R         Power dissipated in a resistance

The third one is the one that surprises people, so it is worth dwelling on: the heat in a cable goes up with the square of the current. Double the current in a cable and you get four times the heating. This is the reason a cable that is fine at 10 A is not merely "a bit warmer" at 20 A, and it is the reason undersized cable does not fail gently.

The water analogy, and exactly where it lies to you#

Voltage as pressure, current as flow rate, resistance as pipe narrowness. It is a good analogy and you should use it. It fails in three specific places, and knowing where it fails is more useful than the analogy itself.

1. Water leaks to the ground; electricity needs a complete loop. Current only flows if there is a path back. This is why a bird is fine on a wire and why a person standing on a concrete floor is not.
2. Water in a pipe moves at the speed of the water; electrical energy moves at nearly the speed of light. The electrons drift slowly, millimetres per second. The push propagates almost instantly. This matters enormously in Class 9 when a signal reflects off the end of a cable.
3. A water pipe does not care about the return path's route; a circuit cares intensely. Where the current goes back is what causes ground loops, hum, and interference. Class 7 is largely about that one sentence.

Wire it before you wire it#

Ten minutes in a browser, with a meter on it. Predict every reading before you press run: the prediction is the exercise and the simulation is only the marker.

Series and parallel: the two ways things connect#

Two components, two ways to wire them, completely different behaviour. Nearly every wiring mistake in a theatre is a series/parallel confusion wearing a costume.

In series, the same current passes through everything, and the voltage divides between them. If one opens, everything stops. Old Christmas lights. A safety chain of emergency stops. A DMX daisy chain is a series topology for its shield and a bus for its data, which is why Class 9 spends an hour on it.

In parallel, the same voltage is across everything, and the current divides. If one opens, the others carry on. Every socket circuit in the building. Every fixture on a bar.

The practical consequences:

The last row of that table is the one that bites. Adding another fixture to a parallel circuit increases the current drawn. People know this. What they do not do is act on it, which is how a 16 A way ends up with 19 A of LED fixtures on it because each one is "only small".

The divider that sags#

This is the circuit that most people build wrong once and never again. Two resistors, half the voltage, and then a load hung on the middle that pulls it somewhere else entirely. A divider is not a power supply, and the reason is visible in about ninety seconds here.

AC, DC, and why the wall is different#

Everything so far has been direct current: a steady push in one direction, which is what a battery and a power supply give you. The mains is not that.

Alternating current reverses direction fifty times a second in Hong Kong, the UK, most of Europe and Asia, and sixty times a second in North America and parts of Japan. It is used because it can be transformed to a different voltage cheaply and efficiently, which is what makes national distribution possible at all.

Three consequences you need today:

1. The number on the wall is an RMS number, not the peak. 220 V RMS peaks at about 311 V. The RMS value is defined as the DC voltage that would produce the same heating, which is exactly why it is the number we use. When you put a scope on the mains in Class 8, you will see the peak, and it will look wrong until you remember this.
2. A meter set to DC will read roughly zero on AC, because the positive and negative halves average out. Getting this wrong is the single most common beginner measurement error, and you will make it at least once in Class 2.
3. AC is what makes hum. Fifty hertz and its harmonics are in the air, in the ground, and in every cable in the building. Class 7 and Class 8 are, in a real sense, four hours of dealing with the consequences of this paragraph.

Going deeperthree phase, and why the dimmer room has it#

Large buildings are fed with three separate alternating supplies, each a third of a cycle apart. It lets three times the power travel down four conductors instead of six, and it makes large motors start smoothly.

For you, in a theatre, three things matter. The voltage between any two phases is about 1.73 times the voltage from one phase to neutral, so a building with 220 V sockets has 380 V between phases, and that will kill you considerably faster. Loads should be balanced across the three phases or the neutral carries the difference. And if you ever see two separate phases arriving at the same piece of scenery, stop, and get the production electrician, because that is a 380 V hazard sitting in a place nobody expects one.

Where the current goes: live, neutral, earth#

This is the model that makes electrical safety make sense, rather than being a list of rules.

• Live carries current from the supply to the load.
• Neutral carries it back. It sits at close to earth potential, but it is not a safety conductor and it is not safe to touch. Under load it will be a volt or two above earth, and if it is broken it can sit at full mains voltage.
• Earth carries current only when something has gone wrong. In normal operation it does nothing at all. Its entire job is to give fault current a path so low in resistance that the protective device trips instantly, instead of the fault current finding a path through a person.

That last sentence is the whole of protective earthing. An earth conductor is not there to "drain electricity away". It is there to make the fault big enough to be noticed by the fuse.

This is also why a missing earth is so dangerous and so invisible: everything works perfectly until the day there is a fault, and then the metalwork is live and nothing trips.

What it costs, and what it needs#

Power is what a thing draws at any instant. Energy is power multiplied by time, and it is what the meter on the building charges for and what a battery holds.

Energy in kilowatt-hours = power in kilowatts × hours

A 500 W lamp for a three hour show is 0.5 × 3 = 1.5 kWh. At a commercial tariff of roughly HK$1.30 per unit that is about two dollars, which is nothing. A hundred of them for a four week run is a real number, and it is the number that made the industry switch to LED far faster than any argument about colour quality.

Three places this arithmetic decides something:

Generator hire. Priced on kVA, not kW, because a generator has to supply the current whether or not the load uses it productively. Divide your total watts by the power factor to get kVA, then add headroom for inrush and for the fact that nobody's load schedule was ever complete.

Battery-powered props. A battery is rated in amp-hours or watt-hours. A prop drawing 200 mA from a 2000 mAh pack runs for about ten hours in theory and rather less in practice, and "rather less" is why you measure it rather than calculating it.

Heat in a room. Every watt of electrical power in a closed room becomes a watt of heat. A dimmer rack dissipating 2 kW is a 2 kW heater, and that is a conversation with whoever sized the air conditioning rather than an electrical problem.

At the bench#

Two hours. You will work in pairs, at low voltage only. Nothing today goes anywhere near mains.

Block A — Prove the three formulae (45 min)#

On a bench supply at 12 V, with a set of known resistors and a lamp:

1. Measure the resistance of three resistors with the meter, cold. Write down the value and the tolerance band.
2. Predict the current each will draw at 12 V. Write the prediction down before you connect it.
3. Measure the actual current. Record both numbers, and the percentage difference.
4. Do the same for the lamp. It will not match your prediction, and it will be out by a factor of several. Do not fix your working. That mismatch is the whole point of Block B.

Block B — The lamp that changes its mind (30 min)#

The lamp's cold resistance is not its hot resistance. A tungsten filament might measure 3 Ω cold and behave like 40 Ω hot. Measure the cold resistance, then measure the voltage and current in operation and calculate the hot resistance from those.

Write down the ratio. Then answer, in your notebook, in one sentence: what does that ratio tell you about the current at the instant you switch a lamp on?

That is inrush, and it is why lamp circuits trip on switch-on and not during the show, and it is what Class 5 opens with.

Block C — Series and parallel, by measurement (45 min)#

Build the four circuits on the sheet: two lamps in series, two in parallel, three in a mixed arrangement, and one with an unintended resistance (a deliberately loose terminal) in the loop.

For each: predict, measure, record, and explain any gap. The loose terminal is the interesting one. Measure the voltage across the terminal itself and calculate the power being dissipated in a connection that is supposed to have none.

Numbers from this class#

Self test with model answers

Answer it yourself first, out loud or on paper, then open the answer. Reading the answer without attempting the question teaches you almost nothing.

1. 1A colleague says a 12 V battery bank is safe because it is low voltage. What is right about that, and what is wrong?
2. 2Why does a cable that is comfortable at 10 A not merely get "a bit warmer" at 20 A?
3. 3A 16 A circuit has six 500 W lamps on it. Is that acceptable? Show the working.
4. 4What is the earth conductor actually for, and why is a missing earth so dangerous?
5. 5Why does adding a fixture to a parallel circuit increase the current, while adding one in series makes everything dimmer?

Note. These are model answers, not the only correct ones. If yours differs and you can defend it with the arithmetic and a measurement, that is worth more than matching the wording.