Cells in Series and Parallel - UNSOLVED PRACTICE SET
Chapter: Current Electricity | Topic: Cells in Series and Parallel
CELLS IN SERIES AND PARALLEL - UNSOLVED PRACTICE SET
Topic: Cells in Series and Parallel
Multiple Choice Questions
Q1. When n identical cells, each of EMF E and internal resistance r, are connected in series, the equivalent EMF is:
- E/n
- E
- nE
- E²
Q2. When n identical cells are connected in series, the equivalent internal resistance is:
- r/n
- r
- nr
- r²
Q3. When n identical cells are connected in parallel, the equivalent EMF is:
- nE
- E
- E/n
- Zero
Q4. When n identical cells are connected in parallel, the equivalent internal resistance is:
- nr
- r
- r/n
- r²
Q5. Series combination of cells is useful when:
- External resistance is very small
- External resistance is very large
- Internal resistance is very large
- EMF required is small
Q6. Parallel combination of cells is useful when:
- External resistance is very large
- External resistance is very small
- High voltage is required
- Internal resistance is negligible
Short Answer Questions
Q7. Derive the expression for the equivalent EMF and internal resistance when two cells are connected in series.
Q8. Derive the expression for the equivalent EMF and internal resistance when two cells are connected in parallel.
Q9. Two cells of EMF 2 V and 3 V and internal resistances 0.5 Ω and 0.3 Ω are connected in series aiding. Calculate the equivalent EMF and internal resistance.
Q10. When should cells be connected in series and when in parallel? Explain with practical examples.
Q11. Two identical cells (E = 1.5 V, r = 0.2 Ω) are connected in parallel to an external resistance of 2 Ω. Calculate the current through the external resistance.
Q12. What happens if two cells of different EMFs are connected in parallel? Explain the difficulty that arises.
Long Answer Questions
Q13. Derive the expression for the current in a circuit containing n identical cells connected in series to an external resistance R. Show that series combination is preferred when R >> r.
Q14. Derive the expression for the current in a circuit containing n identical cells connected in parallel to an external resistance R. Show that parallel combination is preferred when R << r.
Q15. Four identical cells, each of EMF 1.5 V and internal resistance 0.5 Ω, are available.
(a) Calculate the current through an external resistance of 2 Ω when all four cells are connected in series.
(b) Calculate the current when all four are connected in parallel.
(c) Calculate the current when two cells are in series and this combination is in parallel with the other two in series.
(d) For which combination is the current maximum? Explain why.
Numerical / Application-Based Problems
Q16. In a school science project, a student needs to power a small motor that requires 6 V and draws 0.5 A. The student has six identical cells, each of EMF 1.5 V and internal resistance 0.4 Ω.
(a) How should the cells be connected (series, parallel, or mixed) to obtain 6 V? Draw the arrangement.
(b) Calculate the current delivered to the motor for your arrangement.
(c) What is the terminal voltage across the combination? Does it match the motor requirement?
(d) If the motor's resistance is 10 Ω, will it run at the desired speed? If not, suggest a modification.
Q17. A battery bank for a UPS system consists of 12 identical lead-acid cells, each of EMF 2 V and internal resistance 0.05 Ω.
(a) If all cells are connected in series, calculate the equivalent EMF and internal resistance.
(b) If connected to a load of 10 Ω, calculate the current and terminal voltage.
(c) If the cells are arranged in 3 series groups with 4 cells in each group, and these groups are connected in parallel, calculate the equivalent EMF and internal resistance.
(d) For the arrangement in (c), calculate the current through the 10 Ω load. Compare with part (b) and explain which arrangement is better for this load.
Q18. n identical cells, each of EMF E and internal resistance r, are connected to an external resistance R. Show that:
(a) For series connection, I_s = nE/(R + nr).
(b) For parallel connection, I_p = E/(R + r/n).
(c) The current is the same in both arrangements when R = r.
(d) For R > r, series gives more current; for R < r, parallel gives more current. Verify this for n = 4, E = 2 V, r = 1 Ω, and R = 0.5 Ω, 1 Ω, and 5 Ω.