Equivalent Resistance: Series MCQs Quiz | Class 10
This quiz is designed for Class X, Subject Science (Code 086), Unit Practicals (Unit IV). It focuses on Equivalent Resistance: Series MCQs Quiz, covering topics such as determining the equivalent resistance of two resistors connected in series. Answer all 10 questions and click ‘Submit Quiz’ to see your score. You can then download a detailed answer PDF for revision.
Understanding Equivalent Resistance in Series Circuits
The concept of equivalent resistance is fundamental in electrical circuit analysis, especially for understanding how multiple resistors behave when connected in different configurations. This section focuses specifically on resistors connected in series, a common arrangement in various electronic and electrical applications.
What is a Series Circuit?
In a series circuit, components are connected end-to-end along a single path, so the same current flows through each component. There are no junctions to split the current. Imagine a chain where each link represents a resistor; the current flows sequentially through each link.
Key Characteristics of Resistors in Series:
- Current: The current is the same through every resistor in a series circuit. If I is the total current, then I = I1 = I2 = … = In.
- Voltage: The total voltage (potential difference) across the series combination is the sum of the individual voltage drops across each resistor. V_total = V1 + V2 + … + Vn.
- Equivalent Resistance: The equivalent resistance (R_eq) of resistors in series is the sum of their individual resistances.
Formula for Equivalent Resistance in Series:
For ‘n’ resistors (R1, R2, R3, …, Rn) connected in series, the equivalent resistance is given by:
R_eq = R1 + R2 + R3 + … + Rn
This means that connecting resistors in series always increases the total resistance of the circuit.
Example Calculation:
Suppose you have two resistors, R1 = 5 ohm and R2 = 10 ohm, connected in series.
Using the formula: R_eq = R1 + R2 = 5 ohm + 10 ohm = 15 ohm.
So, the two resistors in series can be replaced by a single 15 ohm resistor without changing the circuit’s overall electrical behavior.
Advantages and Disadvantages of Series Circuits:
| Aspect | Series Circuit |
|---|---|
| Total Resistance | Increases |
| Current Flow | Same through all components |
| Component Failure | If one component breaks, the entire circuit breaks |
| Voltage Distribution | Voltage divides among components |
Quick Revision Points:
- Series connection: Components in a single path.
- Current: Constant throughout the series circuit.
- Voltage: Divides across components, sum equals total voltage.
- Equivalent Resistance: Sum of individual resistances (R_eq = R1 + R2 + …).
- Effect of series connection: Increases total resistance.
- Breakdown: Failure of one component stops current flow in the entire circuit.
Practice Questions:
- What happens to the total resistance if you add more resistors in series?
- If a 6V battery is connected to two resistors of 2 ohm and 4 ohm in series, what is the total current flowing in the circuit?
- State one major disadvantage of a series circuit in household wiring.
- Two resistors, R_A and R_B, are connected in series. If R_A = 15 ohm and R_B = 25 ohm, what is their combined resistance?
- In a series circuit comprising three resistors, if the current through the first resistor is 0.5 A, what is the current through the third resistor?
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