Lesson 9: TS Class 10 Physical Science Lesson 9: Electric Current - Important Q&A, Solved Numericals & Objective Bits

⚡ Telangana Class 10 Physical Science — Lesson 9

Electric Current

Complete Chapter Guide: Ohm's Law, Specific Resistance (Resistivity), Series & Parallel Circuits, Kirchhoff's Laws, Solved Power Numericals & Part-B MCQs

📌 Essential Formulas & Circuit Laws

1. Ohm's Law Formula

Potential difference (V) is directly proportional to current (I) at constant temperature:

V = I × R  |  R = V / I  |  I = V / R

2. Specific Resistance (Resistivity ρ)

Resistance (R) depends on length (l), cross-sectional area (A), and material resistivity (ρ):

R = ρ × (l / A)  ⇒  ρ = (R × A) / l

3. Electric Power (P) & Energy (E)

Rate of electrical work done. SI Unit: Watt (W) | Commercial Unit: kWh (1 Unit = 3.6 × 10⁶ J):

P = V × I = I²R = V² / R  |  E = P × t

⚡ Circuit Connections & Kirchhoff's Laws Summary

Key rules governing electrical circuits, potential distribution, and charge flow:

Circuit Analysis Rules At A Glance

1. Series Connection

Current (I): Same in all resistors.
Voltage (V): Splits (V = V₁ + V₂ + V₃).
Equivalent R: R_eq = R₁ + R₂ + R₃.

2. Parallel Connection

Voltage (V): Same across all branches.
Current (I): Splits (I = I₁ + I₂ + I₃).
Equivalent R: 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃.

3. Kirchhoff's Junction Law

Statement: Total current entering a junction equals total current leaving it.
Conservation Law: Based on Conservation of Charge (∑I = 0).

4. Kirchhoff's Loop Law

Statement: Algebraic sum of potential differences around any closed loop is zero.
Conservation Law: Based on Conservation of Energy (∑V = 0).

Ohmic vs Non-Ohmic Conductors: Metals (Copper, Silver) obey Ohm's Law (V-I graph is a straight line passing through origin). Semiconductors (LEDs, Diodes, Electrolytes) are Non-Ohmic (curved V-I graph).

Comparison: Series vs. Parallel Circuit Connections

Parameter	Series Circuit	Parallel Circuit
Electric Current (I)	Remains the same through every component.	Divides among individual parallel branches.
Potential Difference (V)	Divides across each resistor (V = V1 + V2 + ...).	Remains the same across all parallel branches.
Equivalent Resistance (Req)	Increases (Req = R1 + R2 + R3). Greater than largest resistor.	Decreases (1/Req = 1/R1 + 1/R2 + 1/R3). Smaller than smallest resistor.
Failure Impact	If one component fails, the entire circuit breaks (open circuit).	If one component fails, other branches continue working independently.
Practical Application	Decorative festival light strings.	Domestic household wiring.

📝 Short Answer Questions (2 Marks & 4 Marks)

QUESTION 1 - 2 MARKS

Q1. State Ohm's Law. What are Ohmic and Non-Ohmic conductors? Give examples.

Answer:

• Ohm's Law: At constant temperature, the electric current (I) flowing through a metallic conductor is directly proportional to the potential difference (V) across its ends: V = I × R.
• Ohmic Conductors: Conductors that obey Ohm's Law (linear V-I graph). Examples: Metals like Copper, Aluminium, Silver.
• Non-Ohmic Conductors: Conductors that do not obey Ohm's Law (non-linear V-I graph). Examples: Semiconductors, LEDs, Filament bulbs, Electrolytes.

QUESTION 2 - 2 MARKS

Q2. State Kirchhoff's Junction Law and Loop Law. Name the fundamental conservation laws on which they are based.

Answer:

• 1. Junction Law (First Law): The sum of electric currents entering any junction in a circuit equals the sum of currents leaving the junction (∑I = 0). Based on the Law of Conservation of Charge.
• 2. Loop Law (Second Law): The algebraic sum of all potential differences (potential changes) around any closed loop in a circuit is equal to zero (∑V = 0). Based on the Law of Conservation of Energy.

QUESTION 3 - 4 MARKS

Q3. Why are domestic electrical appliances connected in parallel rather than in series? Give three strong reasons.

Answer:

1. Independent Operation: Each appliance gets its own independent switch. Turning off one appliance does not break the circuit for others.
2. Equal Operating Voltage: In a parallel connection, all appliances receive the full mains line voltage (230 V) required for their optimal performance.
3. Lower Total Resistance: Connecting appliances in parallel reduces equivalent resistance, allowing required current to flow without overloading the circuit.

🧮 Solved Board Exam Numericals & Experimental Essays

4 MARKS - SOLVED CIRCUIT & POWER NUMERICAL

Q4. Solve the following electrical problems:
(a) Two resistors of resistance 6 Ω and 12 Ω are connected in parallel across a 12 V battery. Find the equivalent resistance and total current drawn.
(b) An electric bulb is rated 220 V, 100 W. Calculate its resistance and the current drawn when connected to a 220 V supply.

Solution for (a): Parallel Resistors

Given: R₁ = 6 Ω, R₂ = 12 Ω, V = 12 V

1 / R_eq = 1 / R₁ + 1 / R₂ = 1 / 6 + 1 / 12 = (2 + 1) / 12 = 3 / 12 = 1 / 4

R_eq = 4 Ω

Total Current: I = V / R_eq = 12 / 4 = 3 A

Solution for (b): Bulb Resistance & Current

Given: V = 220 V, P = 100 W

Power Formula: P = V² / R ⇒ R = V² / P

R = (220 × 220) / 100 = 48,400 / 100 = 484 Ω

Current: I = P / V = 100 / 220 = 0.45 A

✓ Final Answer:
(a) Equivalent Resistance R_eq = 4 Ω | Total Current I = 3 A
(b) Bulb Resistance R = 484 Ω | Operating Current I = 0.45 A

6 MARKS - EXPERIMENTAL ESSAY

Q5. Describe an experiment to verify Ohm's Law experimentally. State the required apparatus, procedure, V-I graph nature, and conclusion.

Answer:

• Aim: To verify that the potential difference (V) across a metallic conductor is directly proportional to the current (I) flowing through it.
• Apparatus Required: Nichrome wire (resistor), Ammeter, Voltmeter, Rheostat, Battery, Connecting wires, and Plug key.
• Procedure:
  1. Connect the battery, key, ammeter, nichrome wire, and rheostat in series. Connect the voltmeter in parallel across the nichrome wire.
  2. Close the plug key and note the initial readings of Ammeter (I) and Voltmeter (V).
  3. Adjust the rheostat slider to change the current in steps and record the corresponding voltmeter and ammeter readings in a tabular column.
  4. Calculate the ratio V / I for each set of observations.
• Observation & Graph:
  • The ratio V / I remains constant for all observations.
  • A graph plotted taking Current (I) on X-axis and Voltage (V) on Y-axis is a straight line passing through the origin.
• Conclusion: Since V ∝ I, Ohm's Law is verified. The slope of the straight-line graph gives the resistance (R) of the conductor.

🎯 PART-B Objective Bits Bank (10 MCQs)

BIT 1

1. What is the SI unit of Electric Current?

• Volt
• Ampere
• Ohm
• Joule

✓ Correct Option: B (Ampere - A)

BIT 2

2. An Ammeter is always connected in ________, and a Voltmeter is connected in ________ in a circuit.

• Parallel, Series
• Series, Parallel
• Series, Series
• Parallel, Parallel

✓ Correct Option: B (Series, Parallel)

BIT 3

3. What is the SI unit of Specific Resistance (Resistivity ρ)?

• Ohm (Ω)
• Ohm-meter (Ω·m)
• Ohm/meter
• Watt-hour

✓ Correct Option: B (Ohm-meter Ω·m)

BIT 4

4. Kirchhoff's Junction Law is a direct consequence of the Law of Conservation of:

• Energy
• Charge
• Mass
• Momentum

✓ Correct Option: B (Conservation of Charge)

BIT 5

5. If three resistors of 2 Ω, 3 Ω, and 6 Ω are connected in parallel, their equivalent resistance is:

• 11 Ω
• 1 Ω
• 6 Ω
• 0.5 Ω

✓ Correct Option: B (1/R = 1/2 + 1/3 + 1/6 = 6/6 = 1 ⇒ R = 1 Ω)

BIT 6

6. Which of the following is a Non-Ohmic conductor?

• Copper wire
• Silver rod
• Light Emitting Diode (LED)
• Aluminium conductor

✓ Correct Option: C (LED / Semiconductor)

BIT 7

7. Commercial unit of electrical energy 1 kWh is equal to how many Joules?

• 3.6 × 10⁵ J
• 3.6 × 10⁶ J
• 1000 J
• 3600 J

✓ Correct Option: B (3.6 × 10⁶ Joules)

BIT 8

8. When the length of a metallic wire is doubled keeping its cross-sectional area constant, its resistance:

• Becomes half
• Doubles
• Becomes four times
• Remains unchanged

✓ Correct Option: B (Doubles, since R ∝ l)

BIT 9

9. Kirchhoff's Loop Law is based on the Law of Conservation of:

• Charge
• Energy
• Mass
• Angular Momentum

✓ Correct Option: B (Conservation of Energy)

BIT 10

10. What metal is used as the filament in electric bulbs due to its high melting point?

• Copper
• Nichrome
• Tungsten
• Iron

✓ Correct Option: C (Tungsten - Melting point ~3422 °C)