Current Electricity Study Notes

CURRENT ELECTRICITY STUDY NOTES

ELECTRIC CURRENT

• Definition: When a charge flows in a conductor from one place to another, the rate of flow of charge is called electric current.

  • Measured by:

    • Electric current = Rate of flow of charge

    • Mathematical expression: $I = \frac{dq}{dt}$ (if flow is uniform)

    • Instantaneous current: $I = \frac{dq}{dt}$

    • Average current: $I_{av} = \frac{Q}{t}$

Important Points Related to Current

• If n electrons pass through any cross-section in every t seconds, then:
  $I = \frac{ne}{t}$, where $e = 1.6 × 10^{-19} ext{ coulomb}$.

• 1 ampere of current means the flow of 6.25 × 10^{18} electrons per second through any cross-section of the conductor.

• The direction of flow of current is opposite to the flow of electrons.

• The value of current is the same throughout the conductor, irrespective of the cross-section of the conductor at different points.

• The net charge in a current-carrying conductor is zero at any instant of time.

• Electric field outside a current-carrying conductor is zero, but it is non-zero inside the conductor.

• Electric current is a scalar quantity; although in diagrams, it is represented by an arrow, it indicates the direction of flow of positive charges in the wire.

Example Calculations

1. If a charge of $1.6 × 10^{-19}$ coulombs flows per second through any cross-section of a conductor, the current constitutes:

   • $I = \frac{1.6 × 10^{-19} ext{ C}}{1 ext{ sec}} = 1.6 × 10^{-19} ext{ A}$

2. Number of electrons passing through a heater wire in one minute if it carries a current of 8 A:

   • $I = ne/t$

   • $8 = ne/(60)$

   • Solving gives $n = 3 × 10^{20} ext{ electrons}$.

CURRENT DENSITY (J)

• Definition: Current density at any point inside a conductor is defined as a vector having magnitude equal to the current per unit area surrounding that point.

• Mathematical relation:

  • $J = \frac{I}{A}$, where A is the area of cross-section.

Important Points Related to Current Density

1. The direction of J coincides with the direction of current flow.

2. If current density J is uniform for a normal cross-section A, then:

   • $J = \frac{I}{A}$

3. Its SI unit is $A/m^2$ and its dimension is $[L^{-2}A]$.

4. In the case of uniform flow of charge through a cross-section normal to it, the equation is:

   • $I = nqvA$(where n = number density of charge carriers, q = charge, v = drift velocity).

5. Current density relates to the electric field as:

   • $J = σE$\n6. Where σ is the conductivity of the substance.

DRIFT VELOCITY

• Drift velocity is defined as the velocity with which the free electrons are drifted towards the positive terminal under the effect of an applied external electric field:

  • $v_d = rac{I}{nqA}$

  • Where n is number density of free electrons, q is charge of electron, A is cross-sectional area, I is current.

Other Important Relationships

• $I = neAv_d$

• If n = number density of free electrons and A = area of cross-section, total charge crossing through a cross-section over a time interval T can be given as:

  • $Q = I imes t.$

  • The relationship can be derived based on drift velocity.

OHM'S LAW

• Ohm's law states that the current flowing through a conductor is directly proportional to the voltage across it, provided the temperature remains constant:

  • $V = IR$,

  • Where:

    • V = voltage

    • I = current

    • R = resistance of the conductor.

Resistance Calculation and Types

• The total resistance in a circuit is the sum of individual resistances for series connections, and inversely proportional for parallel connections.

  • Series: $R<em>{total} = R</em>1 + R<em>2 + R</em>3 + …$

  • Parallel: $\frac{1}{R<em>{total}} = \frac{1}{R</em>1} + \frac{1}{R<em>2} + \frac{1}{R</em>3}$

Power and Energy in Circuits

• The power consumed in an electrical circuit can be expressed as:

  • $P = VI$ or $P = I^2R$ or $P = \frac{V^2}{R}$

• Units of power: 1 watt = 1 joule/second.

• Energy consumed in a circuit over time t can be given by:

  • $E = Pt$

Measurements and Devices

1. Galvanometer: Measures small currents, deflection proportional to current.

2. Ammeter: Measures large currents, shunted for higher ratings.

3. Voltmeter: Measures potential difference across terminals, connected in parallel.

CONCLUSION

The properties of electrical current, drift velocity, the relationship with resistances, and calculations on nurtured concepts such as power, potential differences, and devices used for measurements provide a comprehensive understanding of electrical phenomena.