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ana111790
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Homework Statement
There are two bulbs, one of 100W and one of 50W and a 120V battery.
First, connect them in parallel, find the resistance and current of each and determine which will shine brighter and by what factor. Next connect them in series, again find the resistance and current of each and determine which will shine brighter and by what factor.
Homework Equations
Parallel circuits have the voltage drop is the same on each loop.
A circuit in series has equal current.
V=IR
P=IV
The Attempt at a Solution
In parallel:
I found the current across each resistor, I=P/V so that current across 100W bulb is .833 A and current across 50W bulb is .417. I then found the resistance of each by R=V/I so resistance of 100W bulb is 144 Ohms and across 50W is 288 Ohms. Because the resistance of 50W bulb is larger it glows brighter, by a factor of 2.
In series:
I set (Voltage across 100W + Voltage across 50W)= 120 V.
Substituting for V=P/I, with I being the same I got: 100/I + 50/I = 120, so I=150/120=1.25 A. I then proceeded to find resistance, R=V/I, so Resistance across the 100W bulb is 100/1.25^2 = 64 Ohms and resistance across 50W bulb is 50/1.25^2 = 32 Ohms. Because it has a larger resistance 100W bulb will shine brighter by a factor of 2.
Can anyone verify this is correct? I want to make sure my concepts are right. Thanks!