Combined Circuit? (See attachment)

Question

idkwut · Answer

attachment

idkwut · Answer

I think I am doing something wrong here. 

12/20 = .60 * 5 = 3

But none of these matches the choices. :<

idkwut · Answer

@whpalmer4

idkwut · Answer

I also got 2.4 and then 4 as answers, lol. Most likely wrong.

whpalmer4 · Answer

resistance of the pair of parallel resistors is $$R_{eff} = \frac{1}{\frac{1}{5~\Omega}+\frac{1}{5~\Omega}} = 2.5~\Omega$$

That gives us a series resistance of $$R_{total} = 5~\Omega + 2.5~\Omega + 5~\Omega = 12.5~\Omega$$and a current of $$i = \frac{V}{R_{total}} = \frac{12.0\text{ V}}{12.5~\Omega} = 0.96~\text{A}$$

with a current of $0.96~\text{A}$ going through the parallel resistance, what will the voltage drop across the parallel resistance be?

idkwut · Answer

@whpalmer4 Sorry, my niece was throwing a fit. Voltage drop = 2.4 since 0.96 * 2.5.

theeric · Answer

I like @whpalmer4 's method. I recommend it more than what I'm about to show you, because @whpalmer4 's method is more general and easily proven.

 Similarly, you can use this method. Note: it is the same exact thing, without bringing up current.
This is a different way of thinking about it. It's the same math.
1. the fact that the resistors will use a proportion of the voltage according to their resistance
2. the fact that all of the voltage drops add up to 12V.

What I mean, is,
The resistance as @whpalmer4 found it is $2.5\ \Omega$ (I agree).

It is in series with two $5\ \Omega$ resistors. So, the total resistance is
$(5+5+2.5)\ \Omega=12.5\ \Omega$

The voltage, $12\rm\ V$, is dropped according to the resistance. You can think of it as volts per ohm. Note: this is current, and it's why we don't have to *think* about current.

So, what is the voltage over $2.5\ \Omega$?

$\rm\dfrac{12V}{12.5\Omega}2.5\Omega=voltage\ across\ parallel\ resistors$

Before, @whpalmer4 did the same division to find the current and then multiplied it by the same resistance. I viewed it as a ratio, he viewed it as a result of Ohm's Law.

theeric · Answer

I agree @IDKwut .

If you have questions about your method, @whpalmer4 's method, or my method, please let me know!

idkwut · Answer

The voltage would be 2.4. since 0.96 * 2.5 = 2.4.

idkwut · Answer

Can you help me on another problem? I will make a new post.

idkwut · Answer

@theEric

theeric · Answer

I will look after I look at a calculus problem.