Resistors in Parallel MCQs Quiz | Class 10
This quiz on Resistors in Parallel MCQs is designed for Class X Science (Code 086), Unit IV: Effects of Current. It covers essential concepts such as equivalent resistance, practical applications, and basic current division in parallel circuits. Test your understanding by attempting all 10 multiple-choice questions. After submitting, you can review your answers and download a detailed PDF answer sheet.
Resistors in Parallel: A Comprehensive Guide
Understanding how resistors behave when connected in parallel is crucial for comprehending electrical circuits. This configuration is widely used in various electronic devices and household electrical systems due to its unique properties.
What is a Parallel Circuit?
In a parallel circuit, two or more components are connected across the same two points, meaning they share the same two nodes. This arrangement ensures that the voltage across each component connected in parallel is the same. The total current flowing from the source divides among the parallel branches, and then recombines when the branches meet again.
Equivalent Resistance in Parallel
When resistors are connected in parallel, the total or equivalent resistance (R_eq) of the circuit decreases. This is because providing multiple paths for the current effectively increases the total cross-sectional area for current flow. The formula for calculating equivalent resistance depends on the number of resistors:
- For two resistors (R1 and R2) in parallel:
1/R_eq = 1/R1 + 1/R2
This can be simplified to: R_eq = (R1 * R2) / (R1 + R2) - For N resistors (R1, R2, …, Rn) in parallel:
1/R_eq = 1/R1 + 1/R2 + … + 1/Rn
A key property is that the equivalent resistance of a parallel combination is always less than the smallest individual resistance in the combination.
Current Division in Parallel Circuits
In a parallel circuit, the total current entering a junction divides among the different parallel branches. The amount of current flowing through each branch is inversely proportional to the resistance of that branch. This means that a branch with lower resistance will have a higher current, and a branch with higher resistance will have a lower current. The sum of currents in all parallel branches equals the total current supplied by the source (Kirchhoff’s Current Law).
For example, if total current is I_total, and we have two resistors R1 and R2 in parallel:
- Current through R1 (I1) = I_total * (R2 / (R1 + R2))
- Current through R2 (I2) = I_total * (R1 / (R1 + R2))
Applications of Parallel Circuits
Parallel connections are widely used due to their distinct advantages:
- Household Wiring: Appliances in homes are connected in parallel. This ensures that each appliance receives the full supply voltage (e.g., 220V in India) and can operate independently. If one appliance fails or is switched off, others continue to function normally.
- Increasing Current Capacity: By connecting multiple batteries or power sources in parallel, the total current capacity can be increased while maintaining the same voltage.
- Safety Devices: Fuses and circuit breakers are often part of a circuit designed to protect parallel branches from overcurrent.
Key Differences: Parallel vs. Series Circuits
| Feature | Parallel Circuit | Series Circuit |
|---|---|---|
| Voltage | Same across each component | Divides across components |
| Current | Divides among branches | Same through each component |
| Equivalent Resistance | Decreases (1/R_eq = sum of 1/R) | Increases (R_eq = sum of R) |
| Component Failure | Other components function | Whole circuit breaks |
Quick Revision Points
- Resistors in parallel have the same voltage across them.
- Current divides among parallel branches.
- Equivalent resistance in parallel is always less than the smallest individual resistance.
- Formula for two resistors: R_eq = (R1 * R2) / (R1 + R2).
- Formula for N resistors: 1/R_eq = 1/R1 + 1/R2 + … + 1/Rn.
- Household wiring is a common application of parallel circuits.
- Parallel connections allow independent operation of devices.
Practice Questions
- Three resistors, 2 Ohm, 3 Ohm, and 6 Ohm, are connected in parallel. What is their equivalent resistance?
- Why are household electrical appliances connected in parallel rather than in series?
- If two resistors are connected in parallel, and one has a resistance of 4 Ohm and the other 6 Ohm, which resistor will have more current flowing through it?
- A 12V battery is connected across two parallel resistors, 4 Ohm and 6 Ohm. What is the voltage across the 4 Ohm resistor?
- If the total current in a parallel circuit with two branches is 5A, and one branch has a current of 2A, what is the current in the other branch?
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