Current Electricity

Electric Current and Flow of Charges

Current is essentially the rate at which electric charge flows through a cross-section of a conductor.

• Definition: The rate of flow of charge per unit time.
• Formula: I = Q / t (where I is current, Q is charge, and t is time).
• Unit: Ampere (A). 1 Ampere = 1 Coulomb / 1 Second.
• Direction: By convention, current flows from Positive to Negative, even though electrons move from Negative to Positive.

Drift Velocity (v_d) and Mobility (μ)

When a battery is connected, electrons don't fly straight; they zig-zag due to collisions.

• Drift Velocity: The average velocity attained by electrons due to an electric field.
• Formula: vd = (eEτ) / m
• Mobility (μ): The drift velocity per unit electric field: μ = vd / E.

Ohm’s Law

The current flowing through a conductor is directly proportional to the potential difference (voltage) across its ends, provided temperature remains constant.

• Equation: V = IR
• V-I Characteristics: For an "Ohmic" conductor, the V-I graph is a straight line passing through the origin. The slope represents the Resistance (R).

Resistance (R) and Resistivity (ρ)

• Resistance: The property of a conductor to oppose current flow.
• Resistivity: A fundamental material property, independent of shape/size.
• Formula: R = ρ (l / A)

Note: If length doubles, R doubles. If thickness (area) doubles, R halves.

Carbon Resistors and Colour Code

Since resistors are small, we use colored stripes to identify values.

Mnemonic: BB ROY of Great Britain had a Very Good Wife.
(Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, White)

Example: Brown (1), Black (0), Red (10²), Gold (±5%) = 10 × 100 = 1000Ω or 1kΩ.

• Electrical Energy (W): Work done to move a charge. W = VIt = I²Rt = V²/R * t
• Electrical Power (P): Rate of energy consumption. P = VI = I²R = V²/R
• Unit: Watt (W).

Comparison: Series vs. Parallel

• EMF (ε): Max potential difference when no current flows (open circuit).
• Terminal Voltage (V): Actual voltage available when circuit is closed.
• Internal Resistance (r): Resistance inside the cell/electrolyte.
• Relationship: V = ε - Ir

Kirchhoff’s Laws

1. Junction Law (KCL): Sum of currents entering a junction = sum of currents leaving. (Conserves Charge).
2. Loop Law (KVL): Sum of potential changes in a closed loop is zero. (Conserves Energy).

Measuring Tools

• Wheatstone Bridge: Balanced when R1/R2 = R3/R4.
• Potentiometer: The "Gold Standard." It draws zero current at the balance point, measuring actual EMF accurately.

Problem: Three resistors of 2Ω, 4Ω, and 6Ω are connected in parallel. This combination is then connected in series with a 5Ω resistor and a 12V battery. Find the total current in the circuit.

Step-by-Step Solution:

1. Find Parallel Resistance (R_p):
   1/R_p = 1/2 + 1/4 + 1/6 = (6+3+2)/12 = 11/12
   R_p = 12/11 ≈ 1.09Ω
2. Find Total Resistance (R_eq):
   R_eq = R_p + 5 = 1.09 + 5 = 6.09Ω
3. Find Total Current (I):
   I = V / R_eq = 12 / 6.09 ≈ 1.97A

Answer: The total current is approximately 1.97A.

In a remote village in Himachal Pradesh, engineers set up a solar-powered micro-grid. They discovered that the battery's internal resistance (r) increases as temperatures drop. To maintain steady voltage (V), they connect batteries in parallel.

To prevent energy loss due to heating (I²R), they use thicker copper wires to increase the cross-sectional area (A), thereby reducing resistance (R). They use a Potentiometer to accurately monitor the solar cells' EMF, ensuring the system remains efficient even in harsh mountain climates.

1. The unit of mobility is:
   a) m/s | b) m²V⁻¹s⁻¹ | c) V/m | d) Ω·m
   Ans: b
2. If the length of a wire is doubled and the area is halved, the resistance becomes:
   a) Same | b) Double | c) 4 times | d) 1/4 times
   Ans: c
3. Kirchhoff's Second Law (Loop Law) is based on the conservation of:
   a) Charge | b) Mass | c) Momentum | d) Energy
   Ans: d
4. The resistance of an ideal voltmeter is:
   a) Zero | b) Very low | c) Infinite | d) 100Ω
   Ans: c
5. In a series circuit, which of the following remains constant?
   a) Voltage | b) Current | c) Resistance | d) Power
   Ans: b
6. The color code for a 1kΩ resistor is:
   a) Brown, Black, Red | b) Red, Red, Red | c) Brown, Black, Orange | d) Black, Brown, Red
   Ans: a
7. Internal resistance of a cell depends on:
   a) Distance between electrodes | b) Concentration | c) Temperature | d) All of the above
   Ans: d
8. The slope of a V-I graph for an Ohmic conductor represents:
   a) Conductance | b) Resistance | c) Power | d) Current
   Ans: b
9. A potentiometer is preferred over a voltmeter because:
   a) It is cheaper | b) It is portable | c) It draws no current at balance | d) It is more sensitive
   Ans: c
10. If three 3Ω resistors are in parallel, the equivalent resistance is:
    a) 9Ω | b) 3Ω | c) 1Ω | d) 0.33Ω
    Ans: c

1. Q: Distinguish between EMF and Terminal Voltage.
   Ans: EMF is the potential difference when no current flows. Terminal voltage is the potential difference when current is flowing (V = ε - Ir).
2. Q: Derive the relation between current and drift velocity.
   Ans: Using I = Q/t and substituting charge carriers, we get I = nAev_d.
3. Q: State Kirchhoff’s Junction Law and explain its physical significance.
   Ans: ΣI_in = ΣI_out. It represents the conservation of electric charge.
4. Q: Why are domestic appliances connected in parallel?
   Ans: So each appliance gets the same voltage, can operate independently, and total resistance stays low.
5. Q: Define Resistivity. How does it differ from Resistance?
   Ans: Resistivity is a material property (independent of shape); Resistance depends on length and area.
6. Q: What happens to the resistance of a semiconductor when temperature increases?
   Ans: It decreases because more charge carriers are released.
7. Q: Explain the principle of a Wheatstone Bridge.
   Ans: It works when the bridge is balanced (R1/R2 = R3/R4), making the galvanometer current zero.
8. Q: Calculate the power consumed by a 10Ω resistor connected to a 5V battery.
   Ans: P = V²/R = 5²/10 = 2.5W.
9. Q: How can you increase the sensitivity of a potentiometer?
   Ans: By increasing the wire length or decreasing the primary circuit current.
10. Q: Draw the V-I graph for a non-ohmic conductor (like a diode).
    Ans: A non-linear curve that does not pass through the origin in a straight line.

• Ohm's Law: V = IR.
• Resistance: R ∝ l, R ∝ 1/A.
• Power: P = VI.
• Kirchhoff: Junction = Charge, Loop = Energy.

Mnemonics to Remember:
• Resistor Color: BB ROY of Great Britain...
• Ohm's Law: Use the Triangle Method (V on top, I and R on bottom).