Series and Parallels

Bill has two identical lamps each of resistance 5 ohms and two 9-volt-batteries. If he wants to light the two lamps for a duration as long as possible, how should he connect the lamps and batteries?

C D A B All four last equally long.

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1 solution

Chew-Seong Cheong
Jul 13, 2015

The trick is to minimize the I 2 R I^2R losses of the load which are the two lamps. That is to minimize the current I I through the lamps. Since by Ohm's Law, I = V R I = \dfrac{V}{R} to minimize I I , we minimize V V and maximize R R . The smallest V V is achieved by connecting the 9-volt batteries in parallel ( V = 9 V V=9 \space V ). To maximize R R we connect the lamps in series ( R = 10 Ω R=10\space \Omega ). The current is I = 0.9 A I = 0.9 \space A . Therefore, the answer is C \boxed{\text{C}} .

Moderator note:

Great observation. It doesn't matter what the voltage / resistance are. We want to minimize V V and maximize R R , which is achieved by the parallel / series configuration respectively.

Thanks. I know that. I was trained as an electrical engineer.

Chew-Seong Cheong - 5 years, 11 months ago

But you said as long as possible not minimum losses or less bright

Jilan Basha - 4 years, 11 months ago

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