it's cheaper and more efficient to use a relay.

They have effectively zero contact resistance, but can switch the current only so fast and only do that so many times before wearing out and are fairly noisy, but even if they fail, they are readily available and easily replaced. This means compromises have to be made on the switching speed

if you wanted to have more granular control you would need power transistors/triacs to be able to switcher the current fast enough to modulate power, these would be more expensive, and less efficient, wasting power and requiring heat sinks for the components and extra circuitry to drive them correctly, increasing costs with no benefit as the food doesn't really care about how power is regulated

induction stoves need high frequency switching to work so they must use electronics, so they always have actual power control rather than "bang-bang" control

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If they didn’t, the control device would heat up as much as the hob.

Using the “water analogy” for electricity, voltage is like water pressure inside a pipe, current is like water flow. The power consumed by an electrical device is the voltage change across it times the current through it.

If a switch is turned off, it holds back the full voltage from the mains, but no current flows through it, so the switch consumes no power, because anything times zero is zero. If it’s turned on, the current is high but it doesn’t hold back the voltage at all, so again no power consumed by the switch.

But if you turn the switch on “halfway”, so it blocks half the mains voltage and lets the other half pass through to the hob, then hob and switch carry the same current across the same voltage change, so the switch consumes as much power as the hob. This is wasteful, but more importantly it’s dangerous, because the switch will produce as much heat as the hob.

This technique is called “pulse modulation”, and it’s incredibly common, not just in stoves. Any time a digital device is controlling a smooth variation of something, the device is usually just switching it on and off. Often the switching happens too fast for humans to notice (like dimmable lighting) or the signal goes through a filter that smooths out the pulses.

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There are fully analog ways to get fractional power that don't require a voltage divider. For example, a variable transformer would work just fine in an electric stove. But a variable transformer is also much larger, more expensive, and less efficient than a cheap relay.

hi, follow-up question to help me understand; would another method (using the dimmable light example) be to have several sets of lights at different light intensities and using say a rotary knob pass current to each set of lights to get sort of a stepped change in light?

using the above method could a switch be turned, say 1/8th of the way on, to waste a minor amount of energy to ease the transition between steps?

thanks for the previous answer!

Thank you for the explanation, I learned something new.

I've actually seen quite a few induction cook-tops that have bang-bang control. Which I don't really understand if they're using switching topologies, like you say. But maybe it's still cheaper to just disable the transistors entirely than to have to design around a variable frequency switching controller?

This is a little incomplete... using a resistor divider or a variac ("halfway" switch) is not the only way to limit current -- switched mode power supplies (AC/DC or DC/DC converters) can limit current and/or voltage to arbitrary, programmable levels with efficiencies of as high as 98% (eg only 2% of energy lost as heat). They turn the output all the way on and all the way off according to a clock signal, with feedback loops connected to sensors at the output to regulate the output voltage or current.

It's still pulse modulation, just done really fast. So instead of using bang-bang at multi-second intervals, you do it at millisecond intervals (or in a modern DC/DC converter, down to ~500 nanosecond intervals)

Why this is not done on a hob/electric stovetop is purely a cost of manufacturing thing. There are solid-state relays that can switch 10 amps and reasonable service lifetimes but they cost $10+ each, and require implementing electronic controls (eg you have to use touch-buttons to set the heat level, or have analog-digital converters reading a rotary knob position...) and various other components, like needing to address current leakage from the solid-state-relay when it's off. The general guideline is you can expect retail value of a piece of electronics to be about 3x the component costs, so for a 4 burner stove it'd likely add at least $150 to the retail price. The benefit to the consumer is almost nil, so justifying the extra cost and complexity is not worth it.

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This might be the case for some electric cookers but not all.

I ran a short experiment on mine. A Beko model D 532, solid plate electric hob. Power consumption was measured with a home smart meter. Each time the ring was set to a given power setting, the power consumption reported by the meter changed within a few seconds then stayed stable over the course of a minute with variations of only +/- 10W at most. The maximum power measured of 1950 W reasonably agrees with the manual which lists a max 2000 for that ring.

Any "bang-bang" control would have to switch on and off on a timescale of seconds or shorter while making no audible noise.

Without disassembling the cooker I cannot say how the control is done, but how it could be done is with multiple heating coils within the solid plate and only some are used at lower power settings. The control "clicks" between numbers with in-between setting not possible, which would be expected with such a control method.

The oven, on the other hand, has a continuously adjustable control. It uses bang-bang control with a thermostat, which is a common approach for thermostatically-controlled heaters. The oven is aiming to maintain a certain air temperature, by contrast the hob settings are for a certain heat output.

Full numbers. All rounded to 10 W with errors of about +/- 10 W.

0: 300 W (Edit: This is the consumption of the other electrical appliances in the house, so needs subtracting from the other figures to get the power used by just the cooker. I checked during the middle of testing and again at the end and it remained consistent.)

1: 500 W

2: 540 W

3: 610 W

4: 1150 W

5: 1440 W

6: 2250 W

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The concept is called Duty Cycle.

We have a 10W of power going through a load for 10% of the time for 1W apparent load over time

It's very easy to turn switches on and off but much harder to continuously vary parameters of a circuit. It can be done but requires more moving parts (sometimes literal moving parts)

Generally speaking it is better to have continuous (analog) control over the system as fast switching creates voltage &/or current spikes in devices which will deteriorate them over time. That being said, a lot of devices don't care about those things and we can change our rate of change during the switching to also minimize damages

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It's a simpler method than trying to actually move the power up and down directly.

Remember, heating elements work by Joule heating. Thus, they satisfy the law P = V^2/R, meaning that the power is proportional to voltage (V) squared, and inversely to resistance (R) (to rough order because technically R depends on temperature T). To modulate the power high to low in the way you're thinking, you have to decrease the voltage. Now given such things are powered by AC, that's not super hard - just use a transformer - but having a transformer in the appliance (and an adjustable one at that) still adds weight and complexity, and thus cost.

But here's the thing. Thanks to thermal inertia, if you instead subject the heating element to an intermittent/pulsed power input, then so long as the pulsing interval is not too large, it will heat up as though it were being subject to a continuous input of heat at a fraction of the maximum power equal to the duty cycle fraction, i.e. how long each pulse lasts versus the total time between pulses. That is to say, the heat capacity of the heating element causes it to act thermally like a low-pass filter, so the temperature response looks like a greatly smoothed version of the power input waveform. Hence if it stays on 30% of the time and is off 70%, e.g. a 0.3 s pulse followed by 0.7 s of off time, then the heating element will act like it is receiving a steady 30% of the input power (or if you like, sqrt(0.30) ~ 55% of the input voltage), with no transformer required, just a switch (maybe a transistor, but still, it's a switch). And switches (incl. transistors) are cheap and easy to make and use.

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fascinating, thanks for the response!

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Resistive power dissipation is given by P = R * I^2 where R is resistance and I is current.

A transistor in an "off" state has a very high resistance but no current flow, so power dissipation is very low to zero.

A transistor in an "on" state--that is, fully on, has a lot of current flowing through it but very little resistance, so power dissipation is low.

A transistor in an intermediate state--the kind of state you'd use for modulating an analog signal--has significant resistance and significant current flow at the same time. That means they dissipate a significant amount of power, and they get hot.

For some things, like audio amplifiers, there's simply no way around this and you have to deal with it by using beefier transistors and providing cooling.

For a lot of applications, including stove burners, it's simpler and cheaper to use pulse width modulation or "bang-bang" controls.

(It could be argued that bang-bang control is just pulse width modulation with a really slow pulse frequency.)

Anyway, in engineering you'll see a lot of things where you wonder, "why don't they do X instead, it seems like it would be better?" In most cases (not all) the answer is that yes, it would be better to do X, but it would also be more expensive, and it wouldn't be enough better to justify the additional cost.