Equivalent Resistance: Parallel MCQs Quiz | Class 10
This quiz tests your knowledge on Class X Science (Code 086), Unit Practicals (Unit IV), focusing on the topic Equivalent Resistance: Parallel MCQs Quiz | Class 10. The questions cover how to Determine equivalent resistance of two resistors in parallel. After submitting your answers, you can review your performance and download a detailed PDF answer sheet.
Understanding Equivalent Resistance in Parallel Circuits
When two or more resistors are connected in parallel, they provide multiple paths for the current to flow. This type of connection is commonly used in household wiring because it ensures that each appliance receives the full supply voltage, and if one appliance fails, the others continue to operate.
Calculating Equivalent Resistance for Parallel Resistors
The equivalent resistance (R_eq) of resistors connected in parallel is always less than the smallest individual resistance in the combination. For any number of resistors connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances:
1 / R_eq = 1 / R_1 + 1 / R_2 + 1 / R_3 + ...
For the specific case of two resistors, R1 and R2, connected in parallel, a simplified formula can be derived:
R_eq = (R_1 * R_2) / (R_1 + R_2)
This formula is particularly useful for quickly calculating the equivalent resistance of two parallel resistors.
Key Characteristics of Parallel Circuits:
- Voltage: The voltage across each resistor in a parallel combination is the same and equal to the total voltage supplied by the source.
- Current: The total current from the source divides among the parallel branches. The current flowing through each resistor is inversely proportional to its resistance (Ohm’s Law: I = V/R). The sum of currents through individual resistors equals the total current from the source.
- Resistance: The equivalent resistance is always smaller than the smallest individual resistance. Adding more resistors in parallel always decreases the total equivalent resistance of the circuit.
- Independent Operation: If one path (resistor) breaks or is disconnected, current can still flow through the other parallel paths.
Comparison: Series vs. Parallel Circuits
Understanding the differences between series and parallel connections is fundamental:
| Feature | Series Circuit | Parallel Circuit |
|---|---|---|
| Resistance | Increases (R_eq = R1 + R2 + …) | Decreases (1/R_eq = 1/R1 + 1/R2 + …) |
| Voltage | Divides across components | Same across all components |
| Current | Same through all components | Divides among branches |
| Impact of Open Circuit | Whole circuit breaks | Other branches continue to work |
Quick Revision Points:
- Parallel connection provides multiple paths for current.
- Voltage is constant across all parallel components.
- Total current is the sum of currents in individual branches.
- Equivalent resistance in parallel is always less than the smallest individual resistance.
- Formula for two parallel resistors: R_eq = (R1 * R2) / (R1 + R2).
Practice Questions:
- Three resistors of 2 ohm, 3 ohm, and 6 ohm are connected in parallel. What is their equivalent resistance?
- If a 20 ohm resistor and a 30 ohm resistor are connected in parallel, calculate the total resistance.
- What happens to the total resistance of a circuit if you add a new resistor in parallel?
- In a parallel circuit, if the voltage across a 5 ohm resistor is 10 V, what is the voltage across another 10 ohm resistor connected in parallel with it?
- Give an example of a real-world application where parallel circuits are essential.
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