Unit 3 Notes in English, FEEE 2004, Polytechnic 2nd Semester

 

3. ELECTRIC AND MAGNETIC CIRCUITS

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Syllabus of this Unit:

1. EMF, Current, Potential Difference, Power and Energy, Ohm’s Law, Combination of Resistances
2. M.M.F, Magnetic Flux
3. Analogy between Electric and Magnetic Circuits

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1. EMF, Current, Potential Difference, Power and Energy, Ohm’s Law, Combination of Resistances

1.1 EMF (Electromotive Force):

• Definition: EMF is the voltage generated by a source like a battery or generator when there is no current flowing.
• Symbol: Denoted by E or V.
• Unit: Volt (V).
• Example: A battery has an EMF of 1.5V. This is the potential difference between the positive and negative terminals of the battery when no current is flowing.

Diagram:

+ (positive terminal)  E (Battery)  - (negative terminal)

• Importance: EMF is the force that drives the current through a conductor when connected to a circuit.

1.2 Current:

• Definition: The flow of electric charge (usually electrons) through a conductor due to a potential difference.
• Symbol: I
• Unit: Ampere (A)
• Formula: $$I = \frac{Q}{t}$$ Where Q is the charge in coulombs and t is the time in seconds.

Example: A 1A current means 1 Coulomb of charge passes through a point every second.

1.3 Potential Difference:

• Definition: The difference in electric potential between two points in a circuit. It is what causes current to flow in the circuit.
• Symbol: V
• Unit: Volt (V)
• Formula: $$V = IR$$Where I is the current in amperes and R is the resistance in ohms.

Example: A potential difference of 5V means there is a 5V difference between two points, causing current to flow through a conductor.

1.4 Power and Energy:

1. Power (P):

   • Definition: The rate at which electrical energy is consumed or generated.
   • Unit: Watt (W)
   • Formula: $$P = VI$$ Where V is voltage and I is current.
   • Example: A 100W light bulb consumes 100 watts of electrical power when connected to a voltage source.

2. Energy (E):

   • Definition: The total electrical energy consumed by a device over time.
   • Unit: Joule (J) or Kilowatt-hour (kWh)
   • Formula: $$E = P \times t$$
     
   • Example: A 60W bulb used for 2 hours will consume $60W \times 2h = 120Wh$ of energy.

1.5 Ohm’s Law:

• Statement: The current flowing through a conductor is directly proportional to the potential difference across it and inversely proportional to the resistance.
• Formula: $$V = IR$$
  
• Example: If a resistor of 5 ohms is connected across a 10V battery, the current flowing through the circuit will be: $$I = \frac{V}{R} = \frac{10}{5} = 2A$$
  

Diagram:

V (voltage) → R (resistor) → I (current)

1.6 Combination of Resistances:

1. Series Combination:

   • Definition: When resistors are connected end-to-end, the total resistance is the sum of the individual resistances.
   • Formula: $$R_{total} = R_1 + R_2 + \dots + R_n$$
   • Example: If three resistors of 2Ω, 3Ω, and 5Ω are connected in series, the total resistance is: $$R_{total} = 2 + 3 + 5 = 10Ω$$
     

2. Parallel Combination:

   • Definition: When resistors are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.
   • Formula: $$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}$$
   • Example: If two resistors of 4Ω and 6Ω are connected in parallel: $$\frac{1}{R_{total}} = \frac{1}{4} + \frac{1}{6} = \frac{5}{12}$$ $R_{total} = \frac{12}{5} = 2.4Ω$
     

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2. M.M.F (Magnetomotive Force) and Magnetic Flux

2.1 M.M.F (Magnetomotive Force):

• Definition: M.M.F is the force that drives the magnetic field through a magnetic circuit, similar to how EMF drives the current through an electric circuit.
• Formula: $$\text{M.M.F} = N \times I$$ Where N is the number of turns in the coil and I is the current flowing through it.

Example: If a coil has 100 turns and the current flowing through it is 2A, the M.M.F is:

$$\text{M.M.F} = 100 \times 2 = 200 \, \text{Ampere-Turns}$$

2.2 Magnetic Flux:

• Definition: Magnetic flux is the total magnetic field passing through a given area.
• Symbol: Φ
• Unit: Weber (Wb)
• Formula: $$\Phi = B \times A$$ Where B is the magnetic flux density and A is the area through which the magnetic field passes.

Example: If the magnetic flux density B is 2 Wb/m² and the area A is 0.5 m², the magnetic flux is:

$$\Phi = 2 \times 0.5 = 1 Wb$$

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3. Analogy Between Electric and Magnetic Circuits

3.1 Electric and Magnetic Circuits Analogy:

• Electric Circuit: Consists of components like resistors, capacitors, and inductors, and is driven by EMF to create current flow.
• Magnetic Circuit: Consists of magnetic components like coils, iron cores, and air gaps, and is driven by M.M.F to create magnetic flux.

Analogy Table:

Electric Circuit	Magnetic Circuit
EMF (Voltage)	M.M.F (Magnetomotive Force)
Current (I)	Magnetic Flux (Φ)
Resistance (R)	Reluctance (Rₗ)
Power (P)	Magnetization Power

• Resistance is analogous to reluctance, which is the opposition to the flow of magnetic flux.
• Current is analogous to magnetic flux.
• EMF is analogous to M.M.F.

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MCQ Questions:

1. What is the unit of EMF?

   • a) Ampere
   • b) Volt
   • c) Watt
   • d) Ohm
   • Answer: b) Volt

2. Which of the following is Ohm’s Law?

   • a) V = I + R
   • b) V = IR
   • c) V = I/R
   • d) V = R/I
   • Answer: b) V = IR

3. What is the unit of Power?

   • a) Joule
   • b) Volt
   • c) Watt
   • d) Ampere
   • Answer: c) Watt

4. The total resistance in a series circuit is the sum of the individual resistances. What is the total resistance for 4Ω, 3Ω, and 5Ω resistors in series?

   • a) 12Ω
   • b) 7Ω
   • c) 6Ω
   • d) 4Ω
   • Answer: a) 12Ω

5. What is the total resistance for two resistors of 3Ω and 6Ω in parallel?

   • a) 1Ω
   • b) 4.5Ω
   • c) 2.4Ω
   • d) 9Ω
   • Answer: c) 2.4Ω

6. What is the formula for calculating Magnetic Flux?

   • a) Φ = B × A
   • b) Φ = I × R
   • c) Φ = E × R
   • d) Φ = M.M.F × A
   • Answer: a) Φ = B × A

7. Which is the unit of Magnetic Flux?

   • a) Tesla
   • b) Weber
   • c) Ampere-Turn
   • d) Volt
   • Answer: b) Weber

8. The MMF is the product of which two quantities?

   • a) Voltage and Current
   • b) Current and Turns
   • c) Voltage and Resistance
   • d) Resistance and Current
   • Answer: b) Current and Turns

9. What is the analogy of Magnetic Flux in an Electric Circuit?

   • a) Voltage
   • b) Current
   • c) Power
   • d) Resistance
   • Answer: b) Current

10. The total resistance of resistors in parallel is always:

    • a) Greater than the largest resistance
    • b) Equal to the sum of all resistances
    • c) Smaller than the smallest resistance
    • d) Dependent on the supply voltage
    • Answer: c) Smaller than the smallest resistance

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Important Practice Questions:

1. Explain the relationship between EMF, Potential Difference, and Current in a circuit.

   • Solution: EMF is the potential difference provided by the source (e.g., battery). The potential difference across the components causes current to flow, and the relationship between them is governed by Ohm’s Law: $V=I\mathrm{R.}$

2. Explain the combination of resistances in series and parallel with examples.

   • Solution: In series, the total resistance is the sum of individual resistances. In parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances.

3. State and explain Ohm’s Law.

   • Solution: Ohm’s Law states that the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. The formula is $V = IR$.

4. Define M.M.F and explain its analogy with EMF in electric circuits.

   • Solution: M.M.F is the driving force for the magnetic field, similar to EMF driving the electric current. The formula is $\text{M.M.F} = N \times I$.

5. Explain the analogy between electric and magnetic circuits.

   • Solution: In an electric circuit, voltage is analogous to M.M.F, current is analogous to magnetic flux, and resistance is analogous to reluctance.