Resistors in Series - UNSOLVED PRACTICE SET

Q7. State the rules for current, voltage, and total resistance in a series circuit. Write the formula for equivalent resistance of resistors in series.

Q8. Three resistors R₁ = 5 Ω, R₂ = 10 Ω, R₃ = 15 Ω are connected in series to a 30 V battery.
(a) Calculate the total resistance.
(b) Find the current flowing.

Q9. In old-style string lights used in Indian festivals (Diwali), all bulbs were connected in series. What was the main disadvantage of this arrangement? Why have modern lights switched to parallel?

Q10. Using the current from Q8 above (series circuit), calculate the voltage drop across each resistor. Verify that the sum of voltage drops equals the battery voltage. 

Q11. A fuse is always connected in series in a circuit — never in parallel. Explain why this is essential for its protective function.

Q12. If the total resistance in a series circuit must be exactly 47 Ω and you only have resistors of 10 Ω, 15 Ω, and 22 Ω available, can you achieve this? Show your working.

Q13. Derive the formula for equivalent resistance of resistors in series. Your derivation must cover:
(a) a diagram description showing three resistors R₁, R₂, R₃ in series with a battery V,
(b) stating that current I is the same through all,
(c) applying Ohm's Law to each: V₁=IR₁, V₂=IR₂, V₃=IR₃,
(d) using V = V₁ + V₂ + V₃ to derive R_s = R₁ + R₂ + R₃, and
(e) stating the key property: total resistance is always greater than the largest individual resistance.

Q14. A series circuit consists of a 12 V battery and three resistors: R₁ = 2 Ω, R₂ = 4 Ω, R₃ = 6 Ω.
(a) Calculate the total resistance.
(b) Calculate the current in the circuit.
(c) Calculate the voltage across each resistor.
(d) Verify Kirchhoff's Voltage Law (KVL): sum of voltage drops = supply voltage.
(e) Calculate the power dissipated in each resistor.
(f) Which resistor dissipates the most power and why?

Q15. Explain why the series circuit arrangement is used for certain electrical components in India but not for domestic appliances.
(a) Why is a fuse always in series?
(b) Why is an ammeter always in series?
(c) Why was the original decorative lighting (series fairy lights) problematic?
(d) Describe a circuit (like a street lamp control) where series connection is actually useful.
(e) What is the main practical disadvantage of series connection for home appliances?

Q16. A series circuit has a 24 V battery and four resistors: 3 Ω, 5 Ω, 7 Ω, 9 Ω.
(a) Find total resistance.
(b) Find current.
(c) Find voltage across each resistor.
(d) The 7 Ω resistor is replaced by an open switch — what happens to current and voltage across each component?

Q17. A student connects a 100 Ω resistor, a bulb of resistance 300 Ω, and a motor of resistance 200 Ω in series to a 180 V supply.
(a) Find total resistance.
(b) Find current.
(c) Find voltage across each component. 

(d) The student says the bulb doesn't glow brightly — explain using the voltage distribution.
(e) What resistance must be added in series to reduce the current to 0.25 A?

Q18. Two resistors are in series across 100 V. The voltage across the first is 40 V and the current is 2 A.
(a) Find R₁.
(b) Find the voltage across R₂.
(c) Find R₂.
(d) Find the total resistance.
(e) If a third resistor R₃ = 10 Ω is added in series, find the new total resistance, current, and voltage across R₃.