 # How much current does an incandescent lamp draw?

One of the questions in Challenge circuit 6 was to find the amount of current a 24V 25W lamp will draw at the rated voltage. The theoretical answer for this question was 1.04 A, and when we measured it, we found it to be close to 1.02 A. But is the response that simple? Let’s thrash it out.

## Resistance of an incandescent lamp is not fixed

Unlike the resistance of a resistor, which is mostly a fixed value, the lamp’s resistance is not always the same. When a voltage is applied to a lamp, the current starts flowing through it and heats the element. As the element heats up, it starts to produce light, but at the same time, its resistance also increases. As the resistance increases, the current decreases – up to a certain point. Once the element reaches a steady state, the temperature and the resistance stop changing, and the current also stops changing. Let’s call this a steady-state current.

The steady-state current depends on the voltage across the lamp. In our previous example of a 24V 25W lamp, the steady-state current was 1.04 A (theoretical). However, if the voltage were 12V instead of 24V, this current value would have been different. It is hard to calculate the steady-state current when the voltage is different from the rated value. This is because it’s hard to predict a lamp’s resistance or power dissipation at a voltage other than the rated value.

## Lamp Steady-State Current at Rated Voltage

Let’s look at the three different incandescent lamps to understand the resistance, current and power dissipation changes.

• 12V 3W
• 24V 25W
• 42V 25W

Before we proceed, we will calculate the steady-state currents each lamp will draw. Similarly, we can find the steady-state current for the remaining two lamps. Here are the results for all three.

12V 3W
0.25 A
24V 25W
1.04 A
42V 25W
0.595 A

Based on the steady-state currents, we can calculate the effective resistance of the lamps using one of Ohm’s law formulas. If we supply the rated voltage to these lamps, their resistance values should be close to the ones listed below.

Lamp Resistance at Rated Votlage
12V 3W
48 Ohms
24V 25W
23.08 Ohms
42V 25W
70.59 Ohms

## Cold resistance of an incandescent lamp and inrush current

Cold resistance refers to its resistance when there is no voltage across the lamp or it hasn’t been powered for some time. The easiest way to find this value is to measure the terminals with an ohmmeter. Here are the results

Lamp Cold Resistance
12V 3W
5.6 Ohms
24V 25W
2.5 Ohms
42V 25W
6 Ohms ### Lamp's Inrush Current

Let’s use Ohm’s law to estimate the current draw of the lamps based on the cold resistances. Do you think they would be different to the steady-state currents? Here is the calculation for one of them We can calculate the current for each using the same formula.

Lamp Estimated Inrush Current Based on Cold Resistance
12V 3W
2.14 A
24V 25W
9.6 A
42V 25W
7 A

As you can see, these values are much higher than the expected steady-state currents. Since the lamps draw these currents only when starting from cold, let’s call these startup currents or Inrush currents.

### How does this affect a circuit?

If we choose circuit components based only on the steady-state current of the lamp, we may face some problems, especially with the control mechanism. Examples of control mechanisms are contacts of a switch, push button or relay.

All contacts have at least a current rating to consider, which is usually combined with a voltage value. If your circuit was to draw more current than this rating, you could damage the contacts. This is in line with the second question of the Challange circuit 6 – would connecting 24V 25W in series with a 1A reed switch be safe. And the response was that it could damage the reed switch. However, this is only considering the steady-state current.

If we consider the inrush current of the lamp of 9.6 A, we will realise that it’s highly likely that the reed switch will get damaged the instant it is activated.

## Can you predict the steady-state current at any voltage?

How much current could a 12V 3W lamp draw at 6V? If the lamp’s resistance were constant, it could be easy to estimate the current – it would be half of the current at the rated voltage. Let’s see if that is the case for these lamps. The table below shows the measured currents at 75%, 50%, and 25% of the rated voltages and their corresponding resistances.

Here is a video of 12V 3W lamp, measuring current and power at different voltages

Here is the table for the 12V 3W lamp

Lamp Measured Current Measured Power Resistance based on measurements
3V (25% of Rated Voltage)
0.104 A
0.31 W
28.8 Ohms
6V (50% of Rated Voltage)
0.157 A
0.94 W
38.22 Ohms
9V (75% of Rated Voltage)
0.198 A
1.78 W
45.45 Ohms
12V (Rated Voltage)
0.234 A
2.81 W
51.28 Ohms

Similar to the video, we conducted experiments for each lamp. I have also included the resistance values that we calculated from the measurements

Here is the table for 24V 25W lamp

Lamp Measured Current Measured Power Resistance based on measurements
6V (25% of Rated Voltage)
0.499 A
2.99 W
12.02 Ohms
12V (50% of Rated Voltage)
0.693 A
8.30 W
17.32 Ohms
18V (75% of Rated Voltage)
0.855 A
15.39 W
21.05 Ohms
12V (Rated Voltage)
0.994 A
23.85 W
24.14 Ohms

And here is the table for 42V 25W lamp

Lamp Measured Current Measured Power Resistance based on measurements
10.5V (25% of Rated Voltage)
0.318 A
3.3 W
33.02 Ohms
21V (50% of Rated Voltage)
0.448 A
9.4 W
46.88 Ohms
31.5V (75% of Rated Voltage)
0.553 A
17.5 W
56.96 Ohms
42V (Rated Voltage)
0.642 A
27 W
65.42 Ohms

Let’s plot all our resistance values to see how linear the resistances are as the voltage changes. Please note: 0% rated voltage in the graph below means cold resistance. From the graph, it seems that the resistance of incandescent lamps is fairly linear after they have been heated up. So it’s easy to predict the current once we know any two points, for example, between 25% and 100%, but in the real world, this is highly impractical.

We can also see that the resistance values are not linear from cold resistance to 25%. This makes sense because the inrush currents of the lamps were quite high compared to all the other values.

## Conclusion

There is a good reason why most loads display their rated voltage and power consumption rather than resistance values. Unlike resistors, which have a fairly constant value at a given temperature, the resistance (or impedance in AC circuits) of loads changes based on various factors. In our case, the heating of incandescent lamp filaments due to the current changed the resistance.

The most important points to consider from the above discourse are

• The operational or steady-state current of the incandescent lamps (and most loads) is usually estimated based on rated voltage and power consumption, rather than their resistance values.
• Inrush current can be estimated using the cold resistance of the incandescent lamps. This can be useful when choosing the circuit components. 