Answers
1.91 V is the correct answer to the given problem.
Let and r be the internal EMF and resistance of the battery.
For the 1500 resistance (say
), the equation for internal EMF of battery is,
where is the current flowing in the circuit with
resistance connected.
The current flowing in the circuit is given as,
with as the terminal voltage in this case.
Similarly, for the 5 resistance (say
), the equation for internal EMF of battery is,
Equating both the equations to find r,
The internal EMF of the battery may be obtained from the second equation for as,
In the case of 7.00 resistor (say R) connected across the battery, the current (I) in the circuit is given as,
The terminal voltage (V) in this case is,
1.91 V is the correct answer to the given problem. Let V_i and r be the internal EMF and resistance of the battery. For the 1500 M Ohm resistance (say R_1), the equation for internal EMF of battery is, V_i = I_1 R_1 + I_1 r where I_1 is the current flowing in the circuit with R_1 resistance connected. The current flowing in the circuit is given as, I_1 = V_1/R_1 with V_1 as the terminal voltage in this case. I_1 = 2.5/1500 times 10^6 = 16.7 times 10^-9 A Similarly, for the 5 Ohm resistance (say R_2), the equation for internal EMF of battery is, V_i = I_2 R_2 + I_2 r I_2 = V_2/R_2 = 1.75/5 = 0.35 A Equating both the equations to find r, I_1 R_1 + I_1 r = I_2 R_2 + I_2 r r = I_1 R_2 - I_2 R_2/I_2 - I_1 = 2.5 - 1.75/0.35 - 1.67 times 10^-9 = 2.14 Ohm The internal EMF of the battery may be obtained from the second equation for V_i as,
.
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