How to find missing resister with a given voltage value?

I have two circuits, where resister voltage are given, and I need to
find resistor value.


first circuit is -- both are serial circuits

E= 24v, R1 = 2ohm, R2=4 ohm, and R3= 24W (watts).

Find R. How do I do this, Also please explain the method.


Second question is

E = 20V, R1=2V, R2=40ohm, R3=32ohm. Find resistor R1 using voltage
divider rule.

This is what I have done so far for;

formula; v1 = R1*E/R1

2v=R1*20v/R1
2V=20V
=10ohm

I use this method on another serial circuit with all the ohms,
current, voltage, and I didn't get the right answer. There are no
answer at the back of the book, and I don't know if I am right.

(E-Mail Removed) wrote:
> I have two circuits, where resister voltage are given, and I need to
> find resistor value.
>
>
> first circuit is -- both are serial circuits
>
> E= 24v, R1 = 2ohm, R2=4 ohm, and R3= 24W (watts).
>
> Find R. How do I do this, Also please explain the method.

You have one simple formula relating I to V for R3. I*V=24,
or I=24/V or V=24/I.
You need to come up with a second formula relating I and V
to R value based on the other two resistors and total
voltage. Then combine these two formulas to solve for R3.

The voltage across R3 must be 24 - R1 drop - R2 drop. Each
of these drops is pretty easy to describe in terms of the
common current, which is also pretty easy to describe in
terms of R3.

> Second question is
>
> E = 20V, R1=2V, R2=40ohm, R3=32ohm. Find resistor R1 using voltage
> divider rule.

The divider rule is

fraction of total voltage that is dropped across Rx
= Rx/Rtotal

So, in this case Vfraction = 2/20 = 0.1
=R1/(R1+R2+R3)

> This is what I have done so far for;
>
> formula; v1 = R1*E/R1
>
> 2v=R1*20v/R1
> 2V=20V
> =10ohm
>
> I use this method on another serial circuit with all the ohms,
> current, voltage, and I didn't get the right answer. There are no
> answer at the back of the book, and I don't know if I am right.
>

(E-Mail Removed) wrote:

> I have two circuits, where resister voltage are given, and I need to
> find resistor value.

You can do this with Ohm's Law.

Do you know it ?

Graham

> I have two circuits, where resister voltage are given, and I need to
> find resistor value.
>
>
> first circuit is -- both are serial circuits
>
> E= 24v, R1 = 2ohm, R2=4 ohm, and R3= 24W (watts).
>
> Find R. How do I do this, Also please explain the method.
>
>
> Second question is
>
> E = 20V, R1=2V, R2=40ohm, R3=32ohm. Find resistor R1 using voltage
> divider rule.
>
> This is what I have done so far for;
>
> formula; v1 = R1*E/R1
>
> 2v=R1*20v/R1
> 2V=20V
> =10ohm
>
> I use this method on another serial circuit with all the ohms,
> current, voltage, and I didn't get the right answer. There are no
> answer at the back of the book, and I don't know if I am right.
>

In both circuits E=I*(R1+R2+R3) and you have to solve for an unknown R,
which means you must eliminate I from the equation.
In the first circuit you are given the power in R3 is 24W which I^2*R3
so that I=sqrt(24/R3) and the equation becomes:
E=sqrt(24/R3)*(R1+R2+R3), or 24=sqrt(24/R3)*(6+R3), which you can now
solve for R3.
In the second circuit you are given the voltage drop across R1 is
2V=I*R1 so that I=2/R1 and the equation becomes E=2/R1*(R1+R2+R3), or
20=2/R1*(R1+72), which you can now solve for R1.