EMF and Internal Resistance of a Cell - UNSOLVED PRACTICE SET

Q7. Distinguish between EMF and terminal potential difference of a cell. When are they equal?

Q8. A cell of EMF 2 V and internal resistance 0.5 Ω is connected to a resistor of 4.5 Ω. Calculate the terminal potential difference.

Q9. Why does a new battery have low internal resistance while an old battery has high internal resistance?

Q10. When is the terminal potential difference of a cell greater than its EMF? Explain with a circuit diagram.

Q11. A cell has EMF 1.5 V. When connected to an external resistance of 2 Ω, the terminal voltage drops to 1.2 V. Calculate the internal resistance of the cell.

Q12. Why can't we measure the EMF of a cell accurately using a voltmeter of finite resistance?

Q13. Derive the relation V = E − Ir for a cell of EMF E and internal resistance r connected to an external resistance R. Draw the circuit diagram and explain the physical meaning of each term.

Q14. Explain how the internal resistance of a cell can be determined experimentally using a voltmeter, an ammeter, and a variable resistance. Draw the circuit diagram and explain the procedure.

Q15. A cell of EMF 3 V and internal resistance 0.2 Ω is connected to an external resistance R.

(a) Calculate the current and terminal voltage when R = 5 Ω.

(b) Calculate the current and terminal voltage when R = 0.5 Ω.

(c) What is the maximum power that can be delivered to the external resistance? At what value of R does this occur?

(d) Verify that maximum power is delivered when R = r.

Q16. In your school lab, you have a battery that you suspect has developed high internal resistance. You perform the following experiment: you connect the battery to various external resistances and measure the terminal voltage each time.

(a) When R = 10 Ω, V = 4.5 V. When R = 5 Ω, V = 4.0 V. Calculate the EMF and internal resistance of the battery.

(b) What current will flow when R = 2 Ω? What is the terminal voltage in this case?

(c) Calculate the power delivered to the external resistance when R = 2 Ω, 5 Ω, and 10 Ω. At which value is the power maximum?

(d) If this battery is used to power a torch bulb rated 3 V, 0.5 A, will the bulb glow at its rated brightness? Explain.

Q17. A student builds a simple circuit with two cells, each of EMF 1.5 V and internal resistance 0.3 Ω, connected in series. This combination is connected to an external resistance R.

(a) Calculate the equivalent EMF and internal resistance of the combination.

(b) Find the current and terminal voltage for R = 2 Ω, 5 Ω, and 10 Ω.

(c) Plot a graph of terminal voltage V versus current I. What is the slope of this graph and what does it represent?

(d) At what value of R is the efficiency of power transfer 50%? What does this mean?

Q18. A cell of EMF E and internal resistance r is connected to a variable resistance R. The power delivered to R is P.

(a) Show that P = E²R/(R + r)².

(b) By differentiating P with respect to R, show that maximum power is delivered when R = r.

(c) Calculate the maximum power if E = 12 V and r = 2 Ω.

(d) Find the efficiency of the cell at maximum power transfer. Why is maximum power transfer not the same as maximum efficiency?