Finding pd given r, R, and emf?

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In summary, to find the potential difference across a 23 ohm load resistor connected to a battery with an emf of 7.99 V and an internal resistance of 0.555 ohms, you can use the equation V=IR, where V is the potential difference, I is the current, and R is the resistance. Simplifying the equation and solving for I, we get I=0.355598. Then, using V=IR again, with R being 23 ohms, we get V=8.187569615 V.
  • #1
ugodzilla
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Homework Statement


What potential difference is measured across
a 23 ohm load resistor when it is connected
across a battery of emf 7.99 V and internal
resistance 0.555 ohms
Answer in units of V


Homework Equations


V=IR
V=emf - Ir


The Attempt at a Solution


V=IR
emf-Ir=IR
(emf/I)-r=R
emf/I=R-r
I=(emf/(R-r))
I=(7.99/((23+.555)-.555)))
I=0.34739

V=IR
V=(0.34739)(23.555)
V=8.182802174
INCORRECT
 
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  • #2
Welcome to Physics Forums.
ugodzilla said:

Homework Statement


What potential difference is measured across
a 23 ohm load resistor when it is connected
across a battery of emf 7.99 V and internal
resistance 0.555 ohms
Answer in units of V

Homework Equations


V=IR
V=emf - Ir

The Attempt at a Solution


V=IR
emf-Ir=IR
(emf/I)-r=R
emf/I=R-r
That should be R+r in that last equation, since you are adding +r to both sides of the equation before it.
I=(emf/(R-r))
I=(7.99/((23+.555)-.555)))
R is simply 23 ohms, not 23+.555
I=0.34739

V=IR
V=(0.34739)(23.555)
V=8.182802174
INCORRECT
 
  • #3
so,
I=7.99/22.445
I=0.355598
then,
V=(0.355598)(23) ?
or V=(0.355598)(23.555)

I don't understand why I'm not supposed to use the total resistance as opposed to just the external resistance.
 
  • #4
I tried out both ways, and each answer was deemed incorrect.
8.385139229
and
8.187569615
 
  • #5
I finally got! I didn't see the comment you made about the mistake in my simplifying! Thanks for the help
 
  • #6
ugodzilla said:
so,
I=7.99/22.445
I don't understand why I'm not supposed to use the total resistance as opposed to just the external resistance.
When you said that "V=emf - Ir", that V is the voltage across the 23 ohm resistor.

And you also said "V=IR" -- the same V here. Since V is the voltage across the 23 ohm resistor, R must be referring to that resistor.

ugodzilla said:
I finally got! I didn't see the comment you made about the mistake in my simplifying! Thanks for the help
You're welcome, glad it worked out. :smile:
 

FAQ: Finding pd given r, R, and emf?

1. How do I calculate pd (potential difference) given r (resistance), R (load resistance), and emf (electromotive force)?

The formula for calculating pd is pd = emf - (r + R). This means that you subtract the sum of the resistance and load resistance from the electromotive force to get the potential difference.

2. Can I calculate pd without knowing the load resistance?

Yes, you can still calculate pd without knowing the load resistance. You just need to know the resistance and emf values. The formula for this scenario is pd = emf - r.

3. How does changing the resistance affect the pd?

Changing the resistance will directly affect the pd. As the resistance increases, the pd will decrease and vice versa. This is because resistance is inversely proportional to current, and pd is directly proportional to current. Therefore, as resistance increases, the current decreases, and the pd decreases as well.

4. What happens to the pd if the load resistance is equal to the resistance?

If the load resistance is equal to the resistance, then the pd will be 0. This is because the formula for calculating pd becomes pd = emf - (r + r), which simplifies to pd = emf - 2r. Since r is equal to R, the equation becomes pd = emf - 2R, which means that the pd will be 0.

5. Can pd be negative?

Yes, pd can be negative. This occurs when the load resistance is greater than the resistance and emf. In this scenario, the pd will be negative, indicating that the current is flowing in the opposite direction.

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