A batter with emf E and internal resistance r is connected to a variable resista

Question

A batter with emf E and internal resistance r is connected to a variable resistance R at point X and Y, as show above on the left. Varying R changes both the current I and the terminal voltate Vxy. The quantities I and Vxy are-measured for several values of R and the data are plotted in a graph, as shown above on the right.
(a) Determine the emf E of the battery.

(b) Determine the internal resistance r of the battery.

(c) Determine the value of the resistance R that will produce a current I of 3 amperes(

d) Determine the maximum current that the battery can produce.

(e) The current and voltage measurements were made with an ammeter and a voltmeter. On the diagram below; show a proper circuit for performing these measurements. Use-A- to reprsent the ammeter and -V- to represent the voltemeter.

Explanation / Answer

I= E/(R+r)
VXY=ER/(R+r)

now, the slope of VXY vs. I curve gives= R

so,

a) At I=1 A, R=4 .

so, E= (4+r)

at I=5A, E=(2+5r)

But E should be constant, so, 4+r= 2+5r

4r=2

r=0.5

E= 4.5V

b)r=0.5

c) R= 1 (putting the values)

d)I max= 4.5/0.5=9 A

e) Ammeter should be connnected in series anywhere, because current is constant in a series circuit. and Voltmeter should be coneected across terminals of R, parallel to R.

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