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Current Electricity

Physics • Chapter 3
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Electric Current ($I$)

Rate of flow of electric charge through a cross-section.

$$ I = \frac{dq}{dt} $$

Unit: Ampere (A). It's a scalar quantity!

Current Direction

Drift Velocity ($v_d$)

Average velocity of free electrons in a conductor under external electric field.

$$ v_d = -\frac{eE}{m}\tau $$

$\tau = $ Relaxation time (time between collisions).

Electron Drift

Relation with Current

$$ I = neAv_d $$

Ohm's Law

Current is directly proportional to potential difference (at constant temp).

$$ V = IR $$
V-I Graph

Limitations

Fails for non-ohmic devices (diodes, transistors, GaAs).

Non Ohmic Graph

Resistivity ($\rho$)

$$ R = \rho \frac{L}{A} $$

Depends on material & temperature, NOT geometry.

Temp Dependence

Metals: $\rho$ increases with T.
Semiconductors: $\rho$ decreases with T.

Electrical Power ($P$)

$$ P = VI = I^2R = \frac{V^2}{R} $$
Power Dissipation

Series: Use $I^2R$ (higher R glows brighter).
Parallel: Use $V^2/R$ (lower R glows brighter).

Carbon Resistors

Color Coding Mnemonic:
B B R O Y Great Britain Very Good Wife

Carbon Resistor
  • Band 1 & 2: Sig Figs (0-9)
  • Band 3: Multiplier ($10^x$)
  • Band 4: Tolerance (Gold 5%, Silver 10%)

Resistors Combo

Series

$$ R_{eq} = R_1 + R_2 + \dots $$

Current is same across all.

Parallel

$$ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots $$

Voltage is same across all.

Resistor Combos

Cells & EMF

EMF ($\varepsilon$): Potential difference when no current is drawn.

Terminal Voltage ($V$): Potential diff when current $I$ is drawn.

$$ V = \varepsilon - Ir $$
Real Battery

Combination of Cells

Series

$$ \varepsilon_{eq} = \varepsilon_1 + \varepsilon_2 $$ $$ r_{eq} = r_1 + r_2 $$

Parallel

$$ \varepsilon_{eq} = \frac{\varepsilon_1/r_1 + \varepsilon_2/r_2}{1/r_1 + 1/r_2} $$ $$ \frac{1}{r_{eq}} = \frac{1}{r_1} + \frac{1}{r_2} $$
Cell Combinations

Kirchhoff's Laws

1. Junction Rule (KCL)

Sum of currents entering = Sum leaving. (Conservation of Charge)

2. Loop Rule (KVL)

Algebraic sum of changes in potential around closed loop is zero. (Conservation of Energy)

Kirchhoff's Laws

JEE Tip: Nodal Analysis

Assign a reference node (0V), name unknown nodes ($x$), and apply KCL:

$$ \sum I_{leaving} = 0 $$
Nodal Analysis

Faster than KVL for complex circuits!

JEE Tip: Symmetry

  • Mirror Symmetry: Points mirror symmetric to axis have same potential.
  • Folding Symmetry: Fold circuit along axis parallel to current flow.
Circuit Symmetry

Wheatstone Bridge

Balanced Condition ($I_g = 0$):

$$ \frac{R_1}{R_2} = \frac{R_3}{R_4} $$
Wheatstone Bridge

Used to measure unknown resistance accurately.

Meter Bridge

Practical application of Wheatstone bridge. Null point at length $l$ cm:

$$ S = R \left( \frac{100 - l}{l} \right) $$
Meter Bridge

Galvanometer Conv.

Into Ammeter

Connect low resistance (Shunt $S$) in parallel.

$$ S = \left( \frac{I_g}{I - I_g} \right) G $$

Into Voltmeter

Connect high resistance ($R$) in series.

$$ R = \frac{V}{I_g} - G $$
Conversion