# Finding emf1, R1 & R2 from a graph

• Omar FTM
In summary, the slope of the / = 1, the slope of the \ = 3/4, and the equation to turn E2(1st battery) to E1 of the first battery are all known.
Omar FTM

## Homework Statement

Both batteries in Figure (a) are ideal. Emf 1 of battery 1 has a fixed value, but emf 2 of battery 2 can be varied between 10.0 V and 100.0 V. The plots in Figure (b) give the currents through the two batteries as a function of 2. The vertical scale is set by is = 0.48 A. You must decide which plot corresponds to which battery, but for both plots, a negative current occurs when the direction of the current through the battery is opposite the direction of that battery's emf. What are (a) emf 1, (b) resistance R1, and (c) resistance R2?

## Homework Equations

1/R = I/V = slope

## The Attempt at a Solution

The / plot seems the 2nd battery while the \ seems the 1st as when the 2nd battery provide more current , the 1st one will provide less current.
The slope (1/R) of the / = 1 >>> R2( of battery ) =1 , the slope of \ = 3/4 >> R1 (of battery) = 4/3.
Using the first point of each plot , At E2 = 10v , the emf1 plot (\) current = 1.2 A & the emf2 plot (/) current = -0.96 A.
Are my steps right so far ? what should I do next ?

#### Attachments

• 2016-12-01 15_40_12-WileyPLUS.jpg
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Hi Omar,
Omar FTM said:
The / plot seems the 2nd battery while the \ seems the 1st
I agree. What about the voltages where ##i_1 = 0 ##, respectively ##i_2 = 0 ## ?
Omar FTM said:
The slope (1/R) of the / = 1 >>> R2( of battery ) =1
I suppose >>> is ##\Rightarrow## ? Anyway: don't agree. Not about the numbers and not about ##R_2##.
Omar FTM said:
slope of \ = 3/4 >> R1 (of battery) = 4/3

So: first fix the numbers, then the interpretation.

Where i=0 , E2(2nd battery) = 40v , E2(1st battery) = 60v. ( what is the equation to turn the E2(1st battery) to E1 of the first battery ) ?
I calculated 1\R using If-Ii\Vf-Vi from the plots , R is V\I ( the inverse ).

This ring a bell for ##i_2=0## ?

Now you re-draw the diagram for ##i_1 = 0## ...

All this gives you a few equations with a few unknowns. From then on it's just math

## 1. What is emf1 in a graph?

Emf1, or electromotive force, is the energy per unit charge required to move a charge through a circuit. It is represented by the y-axis in a graph of emf1 vs. current.

## 2. How do you find R1 and R2 from a graph?

R1 and R2 refer to the resistance values in a circuit. To find R1, you can use the equation R1 = (emf1 - emf2)/I, where emf2 is the intercept of the graph on the y-axis and I is the current. To find R2, you can use the equation R2 = (emf1 - emf2)/I, where emf2 is the intercept of the graph on the x-axis and I is the current.

## 3. What is the relationship between emf1, R1, and R2 in a graph?

The relationship between emf1, R1, and R2 in a graph is linear. This means that as the value of emf1 increases, so do the values of R1 and R2.

## 4. Can you use a graph to determine the values of emf1, R1, and R2 for any circuit?

No, a graph can only be used to determine the values of emf1, R1, and R2 for circuits that have linear relationships between those variables. For more complex circuits, other methods such as circuit analysis may be necessary.

## 5. How can I use the values of emf1, R1, and R2 to analyze a circuit?

The values of emf1, R1, and R2 can be used to calculate important characteristics of a circuit, such as the total resistance and current. This information can then be used to understand how the circuit behaves and make predictions about its performance.

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