Series and Parallel Ciruits

[lampshader]

Homework Statement

What if you were to make a circuit with two 150-Watt light bulbs in parallel -- how much current would flow through each bulb? Compare that to the amount of current which would flow through the bulbs if they were connected in series. Which way would create more light?

Homework Equations

1/R (base eq) = 1 / R (base1) + 1 / R (base2) + 1 / R (base N)

I = E (base eq) / R (base eq)
P (base w) = I^2*R

The Attempt at a Solution

We can find the total resistance by:
1/R (base eq) = 1 / R (base1) + 1 / R (base2)

= 1/96 Ohms + 1/96 Ohms
= 1/48 Ohms = 0.2080 Ohms^-1
= R (base eq) = 1 / 0.2080 Ohms^-1 = 4.8077 Ohms.

We can now find the current by using:

E (base eq) = 12V
R (base eq) = 4.8077 Ohms;

then:

I = E (base eq) / R (base eq) = 12V / 4.8077 Ohms. = 2.496 =~ 2.5 A
P (base w) = I^2*R = (2.5 A)^2 * (4.8077 Ohms) = 30.0481 W

Therefore, 30.0481 Watt’s are flowing through each bulb during a live parallel circuit. To find the current of two 150 Watt light bulbs in a series we can use:

R (base eq) = 96 Ohms + 96 Ohms = 192 Ohms.

and:

I = E (base eq) / R (base eq) = 12V / 192 Ohms = 0.625 A
So, P (base w) = I^2*R = (0.625 A)^2 * 192 Ohms = 0.75 W.


My Conclusion, therefore, is the parallel circuit with two light bulbs has more current than that of the series circuit.

 

[gneill]

The bulbs that are in parallel both receive the the same, full voltage of the supply (parallel components share the same potential difference). So both will produce their rated 150 W when connected in parallel to their recommended supply voltage.

The bulbs that are in series carry the same current, but at half the potential difference (since they are identical bulbs).
Since power varies as the square of the potential difference: P ∝ V² , we can expect the bulbs in series to dissipate 1/4 of the power that the parallel bulbs do, and so produce 1/4 of the light output*.

So the conclusion is that more light is produced with a parallel connection.

*This ignores practical considerations of how a real light bulb behaves when not operating at its designed power level. The resistance of a real filament is temperature dependent, and the portion of the light spectrum that gets the largest share of the available energy shifts with temperature, too.