# Parallel circuits at home

My textbook states that if you have a light bulb turned on and you connected a hair dryer with it in parallel, then the brightness of the light bulb will decrease.

The reason my textbook provided, is that that the conducting wires resemble a very low resistance connected in series with the lightbulb and the hair dryer in a combined series-parallel circuit.

But what should that do with turning on a hair dryer?

Assume a constant supply voltage of $$V_{\rm supply}$$ and the wires which connect the bulb to the voltage supply have a resistance of $$R_{\rm wires}$$.
If the current in the circuit is $$I_{\rm initial}$$ then $$V_{\rm supply} = I_{\rm initial}\,R_{\rm wires} +V_{\rm bulb,initial}$$ where $$V_{\rm bulb,initial}$$ is the voltage across the bulb before the hair dryer was connected to the circuit.

Connect a hair dryer in parallel with the bulb.
The current delivered by the voltage supply will increase because the parallel combination of bulb and hair dryer will have a lower resistance than that of the bulb alone.

$$V_{\rm supply} = I_{\rm final} \,R_{\rm wires} +V_{\rm bulb,final}$$ where $$v_{\rm bulb,final}$$ is the new voltage across the bulb (and the hair dryer).

Since $$I_{\rm final}>I_{\rm initial}$$ then $$V_{\rm bulb,final} < V_{\rm bulb,initial}$$ and so the bulb becomes dimmer when the hair dryer is connected to the circuit.

The effect could be even larger if the voltage supply has an internal resistance such that as the current delivered by voltage supply increases the voltage across the terminals of the voltage supply decreases.

• If the hair dryer is "off" ie no current can flow through it, will that cause a change in resistance? – user207455 May 6 at 8:39
• @SolarMike If the hair dryer does not have a current passing through it then it will not affect the voltage across the bulb but once there is current through the hair dryer this will result in a greater voltage drop across the wires and hence a lower voltage across the bulb.. – Farcher May 6 at 8:58

All conductors delivering current to a load have resistance. The minimum size branch circuit conductor that feeds loads in homes in the U.S. is 14 AWG per the NEC, and has resistance of about 0.25 Ohms per 100 feet.

A 1500 watt hair dryer draws about 12.5 amperes. If connected to the end of a 100 foot long branch circuit conductor, per ohms law ($$V=IR$$) the voltage drop across the hair dryer, and any other load in parallel with it at the end of the run, would be about 3 volts. That's probably enough to observe some dimming of a light bulb.

On the other hand, a 100 watt light bulb by itself draws less than 1 ampere. The voltage drop due to it would be less than 1/4 volt. It would have little effect on other loads connected in parallel to it.

Hope this helps.