# Why Does a Bulb’s Individual Resistance Increase When Wired in Parallel?

When I wire three bulbs in a series, the resistance of each bulb is around three ohms (using R=V/I). If I rewire the same bulbs into a parallel circuit, the resistance of each bulb is slightly over double (solving the same way).

Why does the resistance of each bulb increase when wired in parallel?

• Do your bulbs behave like ohmic resistors or are they nonlinear? – flaudemus Mar 17 '19 at 14:19

The resistance of a light bulb changes with the temperature of the filament in the bulb, and therefore changes with the voltage applied to the bulb. The resistance when it is operating at its maximum voltage may be 10 times as much as when the bulb is "off".

You didn't describe exactly what you did in your experiment, but if you connected the same voltage $$V$$ across the three bulbs in series and in parallel, in the series circuit the voltage across each bulb would be $$V/3$$, and the measured resistance of each bulb would be less.

The resistance of the bulbs do not change at all. It is instead the effective resistance of the circuit that changes.

Call the resistance of a bulb $$R$$ and let your battery supply a voltage $$V$$. That voltage must be dropped over all three bulbs roughly equally, so each one gets a voltage $$V/3$$ for its resistance $$R$$. The total resistance is $$R+R+R=3R$$, which determines the amount of current.

When you wire in parallel, however, the equivalent resistance is determined by

$$\frac{1}{R_{eq}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} \Rightarrow R_{eq} = \frac{R}{3}.$$

This is much less, so more current flows. In addition, since you've now wired in parallel, each bulb gets a voltage $$V$$ dropped across it, rather than $$V/3$$. So 3 times the current flows, and 3 times the voltage is dropped: that means the resistance of each bulb stays the same.

Again, it isn't the individual bulbs whose resistance changes. It's that the circuit is completely different, so the voltages, currents, and equivalent resistance of the circuit change. Be careful in analyzing circuits.

• The resistance of an incandescent light bulb is not constant. It varies a lot depending on the voltage applied to the bulb. – alephzero Mar 17 '19 at 12:23
• To me, the question read as if asked by someone in an intro lab experimenting with series vs. parallel circuits. Typically in labs, they use these tiny incandescent bulbs and small currents/voltages, and in that range the resistance certainly does not change by a factor of two or more (I just measured it recently). That's what I had pictured in my mind. Still, you're right, and the OP should be more specific. – flevinBombastus Mar 17 '19 at 12:28
• Re, "tiny incandescent bulbs," The fact that the bulbs are tiny doesn't change anything. Even in a "tiny" flashlight bulb, the tungsten filament still gets white hot under the bulb's normal operating conditions, and the bulk resistivity of white hot tungsten is much higher than the bulk resistivity of room-temperature tungsten. – Solomon Slow Mar 17 '19 at 14:08
• @flevinBombastus It's a fair comment that often in intro labs the bulbs are run at significantly less than their rated voltage, simply to avoid too many blown bulbs when intro students make mistakes, and therefore the filaments never reach their normal operating temperature. But the effect is still there, and we don't know the details of what the OP did. – alephzero Mar 17 '19 at 17:12