Chapter 4 — Effects of Electric Current
All equations use MathJax for perfect fractions, exponents and division — readable on phones.
Can you recall?
- How do we decide if a material is a good conductor or an insulator?
- Iron is a conductor, yet touching a loose iron piece on ground doesn’t shock us — why? (No potential difference across your body.)
Energy Transfer in an Electric Circuit
Consider a cell, a resistor \(R\) and a closed circuit. Let the potential at end \(A\) be higher than at \(B\) (\(V_{AB}=V_A-V_B\)). When charge \(Q\) moves from \(A\) to \(B\), work done by the source is
If this happens in time \(t\), the current is \(I=\dfrac{Q}{t}\) and the electrical power delivered is
The energy delivered in time \(t\) becomes heat in the resistor:
Using Ohm’s Law \(V_{AB}=IR\), Joule’s heating forms:
Unit of Electrical Power
Electrical energy in the household is measured in kWh (Unit):
Heating Effect of Electric Current
When current flows through a resistor, it produces heat: \(H=I^2Rt\). This is used in heaters, boilers, cookers (nichrome coil), and bulbs (tungsten filament at \(\sim 3400^\circ\text{C}\)).
Fuse, Short Circuit & Overloading
- Short circuit: Live and neutral accidentally touch → very large current → intense heating → fire risk.
- Fuse wire: Low-melting wire in series; excessive current melts it and opens the circuit (protection).
- MCB: Miniature Circuit Breaker trips open automatically on overload/short circuit; can be reset.
- Earth wire: Safe path for leakage currents to ground.
Magnetic Effects of Electric Current
Oersted’s Observation
A compass needle near a current-carrying wire deflects — showing a magnetic field around the wire. Stronger current → stronger field.
Right-Hand Thumb Rule
Hold the conductor in your right hand with thumb along current; curled fingers show direction of concentric magnetic field lines.
Field of a Circular Loop
A loop produces magnetic lines of force that add up at the centre; \(n\) turns give roughly \(n\) times the field (for same current).
Solenoid
A long coil (many turns): field inside is nearly uniform, like a bar magnet with distinct \(N\) and \(S\) poles. Inserting soft iron core increases field strength.
Force on a Current-Carrying Conductor in a Magnetic Field
When a conductor carrying current \(I\) is kept in a magnetic field \(\vec{B}\), a force acts on it. The force direction is perpendicular to both \(\vec{B}\) and current direction, and is maximum when current ⟂ field.
Fleming’s Left-Hand Rule
- Index finger → magnetic field (\(B\)),
- Middle finger → current (\(I\)),
- Thumb → force on conductor.
Electric Motor — Principle & Working
Principle: A current-carrying coil in a magnetic field experiences forces on its two sides, producing rotation.
Construction
- Rectangular coil (ABCD) between magnetic poles \(N\) and \(S\).
- Split-ring commutator (two halves X & Y) on axle; carbon brushes (E, F) maintain contact.
Working
With current through the coil, side AB is pushed down, CD up (by left-hand rule) → coil rotates. After half-turn, commutator reverses current in the coil so torque remains in same rotational sense → continuous rotation (mechanical energy output).
Electromagnetic Induction (EMI)
Faraday showed (1831): an induced current appears in a conductor when the magnetic environment of the conductor changes.
Key Observations
- Move wire in a magnetic field → galvanometer deflects.
- Move magnet near a coil → deflection (direction depends on motion).
- Switch current in a nearby solenoid on/off or vary it → induced current in adjacent coil.
Fleming’s Right-Hand Rule (for induced current)
- Thumb → motion of conductor,
- Index → magnetic field direction,
- Middle → induced current direction.
Alternating Current (AC) vs Direct Current (DC)
- DC: flows in one direction (can be steady, increasing or decreasing with time, but non-oscillatory).
- AC: changes direction periodically; in India, frequency \(f=50\,\text{Hz}\) (50 cycles per second), sinusoidal.
- AC is preferred for long-distance transmission due to lower losses and transformer use.
- Household supply is AC.
Electric Generator
Principle: Mechanical rotation of a coil in a magnetic field changes magnetic flux through it → induced emf (EMI) → current in external circuit.
AC Generator
- Coil ABCD rotates between poles; ends connect to slip rings \(R_1,R_2\) and brushes \(B_1,B_2\).
- Each half-turn reverses induced emf polarity → alternating current in external circuit.
DC Generator
- Use a split-ring commutator instead of slip rings so that external connections swap every half-turn.
- External current remains in the same direction (pulsating DC).
Solved Examples
Example 1 — More heat with shorter coil?
A 6 m nichrome wire (coil) has \(R=22\,\Omega\) on \(220\,\text{V}\). If cut to half length, what happens to power?
Answer: Half length → half resistance → double power → more heat.
Example 2 — Find voltage from power & resistance
Heat produced \(=400\,\text{J/s}=400\,\text{W}\) in \(R=9\,\Omega\). Find \(V\).
Example 3 — Iron at two settings
At \(V=220\,\text{V}\): high power \(P_1=1100\,\text{W}\), low power \(P_2=330\,\text{W}\). Find currents & resistances.
Example 4 — Bulb wattage & units consumed
At \(V=220\,\text{V}\) and \(I=0.45\,\text{A}\):
Quick Checks
- Derive \(H=\dfrac{V^2 t}{R}\) from \(P=VI\) and \(V=IR\).
- State the right-hand thumb rule and Fleming’s two rules succinctly.
- Why is the field inside a long solenoid uniform?
- Why is AC preferred for transmission over long distances?
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Chapter 4 — Exercise Solutions
1) Tell the odd one out (with reason)
- Fuse wire, bad conductor, rubber gloves, generator
Odd: Generator — it produces electricity. The others relate to safety/protection: rubber gloves and “bad conductors” (insulators) prevent shock; fuse wire protects circuits by melting on overcurrent. - Voltmeter, Ammeter, Galvanometer, Thermometer
Odd: Thermometer — measures temperature, while the others measure electrical quantities (V, I, tiny I). - Loudspeaker, Microphone, Electric motor, Magnet
Odd: Magnet — a passive magnetic material. The others are electromechanical transducers/devices (convert energy between electrical ↔ mechanical/sound). - Motion of the coil around an axle in an electric motor vs Generation of current in a coil due to relative motion with a magnet
Odd (by concept): the motor motion is magnetic force on current (motor effect), whereas the other is electromagnetic induction (induced emf due to changing flux). Different principles.
2) Construction & Working (with neat labelled diagrams)
(a) Electric Motor
Principle: A current-carrying coil in a magnetic field experiences forces on its sides, producing a torque (Fleming’s left-hand rule). The split-ring commutator reverses the coil current every half turn, keeping the torque in the same rotational sense → continuous rotation.
Construction: Rectangular coil on an axle, placed between magnets (N–S), split-ring commutator on axle, carbon brushes E & F, DC supply.
Working: Side AB experiences downward force; side CD experiences upward force → coil rotates. After half-turn, commutator swaps connections so torque continues in same direction.
(b) Electric Generator (AC)
Principle: Electromagnetic induction — rotating the coil in a magnetic field changes flux through the coil → induced emf → alternating current.
Construction: Coil ABCD on axle between magnets; ends connected to slip rings \(R_1, R_2\); stationary brushes to external circuit.
Working: As coil rotates, induced emf reverses every half turn → AC in the external circuit.
3) Electromagnetic induction means …
Correct concept: Induced emf/current in a conductor whenever the magnetic flux through it changes (due to relative motion of magnet & coil or changing current nearby).
4) Difference between AC generator and DC generator
| Feature | AC Generator | DC Generator |
|---|---|---|
| Output | Alternating current (reverses every half-rotation) | Pulsating DC (same external direction) |
| Collector | Slip rings (continuous) | Split-ring commutator (segments swap every half turn) |
| External current direction | Alternates | Unidirectional |
| Graph | Sinusoidal \(~\) | Pulsating (rectified) waveform |
| Use cases | Power stations, household AC | DC supplies (limited), dynamos |
5) Which device is used to produce electricity? Describe with diagram.
Answer: Electric Generator — here, we show a DC Generator (with split-ring commutator).
Working: Coil rotates in magnetic field → changing flux induces emf (Faraday’s law). Split-ring commutator keeps the external current unidirectional.
6) Short circuit — formation & effect
Formation: Live and neutral conductors accidentally come into direct contact (damaged insulation/fault), creating a very low-resistance path.
Effect: Huge current flows \((I=\dfrac{V}{R_{\text{very small}}})\) → excessive heating, sparks, fire hazard. Fuse/MCB disconnects to protect circuit.
7) Scientific reasons
- (a) Tungsten in bulb filaments: Very high melting point (\(\sim 3400^\circ\text{C}\)), sufficient resistivity, emits bright light when white-hot, withstands evaporation in inert gas.
- (b) Nichrome in heaters: High resistivity (more heat for same length), high melting point, forms protective oxide layer (doesn’t oxidize rapidly), mechanically stable when hot.
- (c) Copper/Aluminium for transmission: Very low resistivity (lower \(I^2R\) losses), ductile, economical (Al), good conductivity (Cu).
- (d) Billing in kWh, not joule: 1 kWh \(=3.6\times10^{6}\) J — convenient practical unit matching appliance ratings and usage durations.
8) Magnetic field near a long straight current-carrying conductor
Correct option: d) The magnetic lines of force are in concentric circles with the wire as centre, in a plane perpendicular to the conductor (Right-hand thumb rule).
9) Solenoid — definition & comparison with bar magnet
Solenoid: A long, tightly wound helical coil of insulated wire. When current flows, it produces a magnetic field similar to a bar magnet — one end behaves like \(N\) pole, the other as \(S\) pole; the field inside is nearly uniform and parallel.
- Similarity: Distinct poles; external field lines go \(N \to S\); internal field is strong and nearly uniform.
- Difference: Solenoid’s field strength can be varied by current/turns; adding soft iron core greatly increases field.
10) Name these diagrams & explain the concept
- (a) Electromagnetic Induction (EMI): Current is induced in a coil when magnetic flux through it changes (move magnet/coil or vary nearby current). Direction by Fleming’s right-hand rule.
- (b) Electric Motor Action: A current-carrying conductor in a magnetic field experiences a force (Fleming’s left-hand rule) → rotational motion of the coil.
11) Identify the figures & explain their use
As the original figures aren’t included, standard relevant items are described:
- (a) Fuse/MCB: Protective device that opens the circuit on overcurrent/short circuit, preventing fire hazards.
- (c) Slip Rings / Split-ring Commutator: Slip rings deliver AC from a rotating coil (AC generator). Split-ring commutator reverses coil connections each half turn to obtain unidirectional DC (motor/DC generator).
12) Numericals — solved
(a) Find resistance
Heat rate (= power) \(P=100\,\text{W}\), current \(I=3\,\text{A}\). Using \(P=I^2R\):
(b) Current in main for parallel bulbs (100 W & 60 W at 220 V)
In parallel: \(I_{\text{total}}=I_1+I_2=\dfrac{P_1}{V}+\dfrac{P_2}{V}\).
(c) Who spends more energy?
- TV: \(500\,\text{W}\times 30\,\text{min}=500\times 0.5\,\text{h}=250\,\text{Wh}\).
- Heater: \(600\,\text{W}\times 20\,\text{min}=600\times \dfrac{1}{3}\,\text{h}=200\,\text{Wh}\).
Answer: TV set uses more electrical energy.