# Variable Resistror, Calculating Vo

• Jreyes613
In summary, the conversation discussed solving for the voltage and internal resistance in a circuit with a variable resistor connected to a battery. The graph provided showed data for the current and resistance values. Using Ohm's Law, the equation I=Vo/(R+r) was used to solve for the voltage and internal resistance by setting up two equations with known values from the graph. The resulting internal resistance was found to be one ohm.
Jreyes613

## Homework Statement

A variable resistor, R, is connected to the terminals of a battery (dashed box in the diagram). The graph below shows data collected in the circuit as R is varied. What is V0, in volts?
What is the internal resistance, r, in ohms?

Ohm's Law

## The Attempt at a Solution

I know that for this case, Vo will be found where the current is calculated to be at its lowest.
from the graph that i am given, It is not clear where it will equal zero, as for the internal resistance, i know that I=ε/r
so
-r=dV/dI
the slope of a V vs I graph will give the internal resistance.

#### Attachments

• Screen shot 2012-03-15 at 6.49.31 PM.png
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Do you have a circuit diagram that you can post? Your graph shows current versus resistance; is the resistance that of the variable resistor? How were they measured or determined?

oops! i forgot to click attach on the second file.
new here :)

Jreyes613 said:
oops! i forgot to click attach on the second file.
new here :)

No problem I see a voltmeter in the circuit, but no current meter. How were the values for the current versus resistance plot obtained?

these were given to me! this is all the information given.

Jreyes613 said:
these were given to me! this is all the information given.

Okay, fair enough. In that case, I'd suggest that the first thing to do would be to write an expression for the current in the circuit assuming that the cell has voltage Vo, with resistors R and r as shown.

okay, so i have the equation I=V/R

since the resistors are in parallel,
(1/Req)=(1/R+1/r)
take the inverse of both sides to get Req
so i get
I=Req(Vo)

Is this right?

Jreyes613 said:
okay, so i have the equation I=V/R

since the resistors are in parallel,
(1/Req)=(1/R+1/r)
take the inverse of both sides to get Req
so i get
I=Req(Vo)

Is this right?

The resistors are not in parallel; the battery cell is between two of their leads so they are not connected to each other at both ends.

okay, so it would still be
I=Req(Vo)
Req= R+r
right?

Jreyes613 said:
okay, so it would still be
I=Req(Vo)
Hmm. Not quite. Ohm's law: V = I*R, so that I = V/R.
Req= R+r
right?
Sure. But write the equation without replacing R and r with Req; you want to have "access" to those variables as you proceed.

okay yes, ( i saw my bad re arranging in the equation)

So I will end up with
I=Vo/(R+r)

I am still in the mist here... i am not sure how to calculate each individual resistor since i am not given their individual values.

Jreyes613 said:
okay yes, ( i saw my bad re arranging in the equation)

So I will end up with
I=Vo/(R+r)

I am still in the mist here... i am not sure how to calculate each individual resistor since i am not given their individual values.

Ha! That's where the graph comes in. You can read off convenient pairs for R and I and build yourself a couple of equations using the expression above as a template. Two unknowns require two equations.

!
thank z, me and my friend used I=Vo/(R+r) to solve for Vo,
Vo=I(R+r)
got two equations
Vo=5.25(r) *since when R=0, I=5.25
Then i used another point
Vo=1.5(2.5+r)
and solved for Vo.
With this, i was able to solve for my internal resistance to equal one.
:) thank you gneill!

Jreyes613 said:
!
thank z, me and my friend used I=Vo/(R+r) to solve for Vo,
Vo=I(R+r)
got two equations
Vo=5.25(r) *since when R=0, I=5.25
Then i used another point
Vo=1.5(2.5+r)
and solved for Vo.
With this, i was able to solve for my internal resistance to equal one.
:) thank you gneill!

## 1. What is a variable resistor?

A variable resistor is an electronic component that can change its resistance value when an external force is applied, such as by turning a knob or sliding a lever.

## 2. How does a variable resistor work?

Variable resistors work by changing the length or cross-sectional area of the resistive material in the circuit. This changes the flow of current and therefore the resistance in the circuit.

## 3. What is Vo in relation to a variable resistor?

Vo (voltage output) is the voltage that is measured across the variable resistor. It is dependent on the resistance value of the variable resistor and the current flowing through it.

## 4. How do you calculate Vo in a circuit with a variable resistor?

To calculate Vo, you will need to know the resistance value of the variable resistor (R) and the current flowing through it (I). You can then use Ohm's Law (V=IR) to calculate the voltage across the variable resistor.

## 5. What are some common uses for variable resistors?

Variable resistors are commonly used in electronic devices to control the amount of current or voltage in a circuit. They are also used in audio equipment to adjust volume, in lighting systems to control brightness, and in industrial applications for precise control of motor speeds.

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