Resistors in Parallel - UNSOLVED PRACTICE SET
Chapter: Electricity | Topic: Resistors in Parallel
RESISTORS IN PARALLEL - UNSOLVED PRACTICE SET
Topic: Resistors in Parallel
Multiple Choice Questions
Q1. When resistors are connected in parallel, the equivalent resistance is:
- Greater than the largest individual resistance
- Equal to the sum of all resistances
- Less than the smallest individual resistance
- Equal to the smallest resistance
Q2. In a parallel circuit, the voltage across each resistor is:
- Different for each resistor
- The same — equal to the supply voltage
- Divided proportionally to resistance
- Zero for high-resistance components
Q3. In a parallel circuit, the total current is:
- The same through each branch
- Equal to the current through the branch with least resistance
- The sum of currents through all branches
- Equal to the voltage divided by the largest resistance
Q4. Two equal resistors of 10 Ω each are connected in parallel. The equivalent resistance is:
- 20 Ω
- 10 Ω
- 5 Ω
- 100 Ω
Q5. Adding more resistors in parallel to a circuit:
- Increases the total resistance
- Decreases the total resistance and increases current from source
- Has no effect on total resistance
- Increases voltage at each resistor
Q6. In a parallel circuit, if one branch is disconnected (open circuit):
- All other branches also go off
- The total resistance decreases
- Current through other branches is unaffected — they continue normally
- The voltage across other branches drops
Short Answer Questions
Q7. State the rules for current, voltage, and equivalent resistance in a parallel circuit. Write the formula: 1/R_p = 1/R₁ + 1/R₂ + 1/R₃.
Q8. Three resistors of 6 Ω, 3 Ω, and 2 Ω are connected in parallel. Calculate the equivalent resistance.
Q9. Why are domestic appliances in Indian homes connected in parallel rather than in series? Give two practical reasons.
Q10. A 220 V supply is connected to three parallel branches: a fan (220 Ω), a TV (110 Ω), a lamp (440 Ω). Calculate the current through each branch and the total current.
Q11. Explain using the formula why the equivalent resistance of a parallel combination is always less than the smallest individual resistance.
Q12. A voltmeter must be connected in parallel with a component. Explain why, using the concept of parallel circuits and the requirement that it should not disturb the existing current.
Long Answer Questions
Q13. Derive the formula for equivalent resistance of resistors in parallel. Your derivation must cover:
(a) a circuit diagram description with three resistors R₁, R₂, R₃ in parallel across voltage V,
(b) stating that voltage is the same across each,
(c) applying Ohm's Law to each branch: I₁=V/R₁, I₂=V/R₂, I₃=V/R₃,
(d) using I = I₁+I₂+I₃ to derive 1/R_p = 1/R₁+1/R₂+1/R₃, and
(e) explaining physically why R_p < R₁, R₂, R₃ (more paths available for current).
Q14. A parallel circuit has a 24 V supply and three resistors: R₁ = 4 Ω, R₂ = 6 Ω, R₃ = 12 Ω.
(a) Calculate the equivalent resistance.
(b) Calculate the current through each branch.
(c) Calculate the total current.
(d) Verify: total current = supply voltage / equivalent resistance.
(e) Calculate the power dissipated in each resistor.
(f) Which resistor dissipates the most power? Is the highest-resistance or lowest-resistance component dissipating more?
Q15. Describe the wiring of a typical Indian home in terms of parallel circuits.
(a) Explain why each room's circuit is in parallel with others.
(b) Why does switching off the fan not affect the TV or lights?
(c) Why can each appliance receive full 220 V even though multiple appliances are running?
(d) Why does the total current increase when more appliances are switched on, and what risk does this create?
(e) How does a main switch (main circuit breaker) protect the entire home's parallel circuit?
Numerical / Application-Based Problems
Q16. A household has four appliances in parallel on a 220 V circuit: Geyser (R = 44 Ω), washing machine (R = 55 Ω), microwave (R = 110 Ω), and lamp (R = 220 Ω).
(a) Calculate current through each.
(b) Calculate total current.
(c) Calculate equivalent resistance.
(d) If the circuit breaker trips at 15 A, is the circuit safe?
Q17. Two resistors are connected in parallel across 60 V. R₁ = 20 Ω draws current I₁, and R₂ draws 1 A. The total current is 4 A.
(a) Find I₁.
(b) Find R₂.
(c) Calculate the equivalent resistance.
(d) Verify using R_p = V/I_total.
(e) A third resistor R₃ is added in parallel, causing total current to rise to 5 A. Find R₃.
Q18. A circuit board has resistors of 10 Ω, 20 Ω, and 30 Ω.
(a) Find equivalent resistance when all three are in parallel.
(b) Find equivalent resistance when all three are in series.
(c) For the same 12 V supply, compare the total current in each arrangement.
(d) In which arrangement does the source deliver more power? Show calculation.
(e) Which arrangement would be safer for delicate components that need low current?