Below are important formulas and concepts from the chapter « Electricity » for Grade 10 NCERT, expanded to cover approximately two pages worth of content. Each formula is explained with its variables:

 1. Electric Current (I)

Formula:

\( I = \frac{Q}{t} \)

Description:

Electric current (I) is the flow of electric charge. It is measured in amperes (A).
\( I \): Current in amperes
\( Q \): Charge in coulombs (C)
\( t \): Time in seconds (s)

 2. Ohm’s Law

Formula:

\( V = IR \)

Description:

Ohm’s Law states that the voltage (V) across a conductor is proportional to the current (I) flowing through it, with resistance (R) as the constant of proportionality.
\( V \): Voltage in volts (V)
\( I \): Current in amperes (A)
\( R \): Resistance in ohms (Ω)

3. Resistance (R)

Formula:

\( R = \rho \frac{L}{A} \)

Description:

Resistance of a conductor depends on its material and dimensions.
\( R \): Resistance in ohms (Ω)
\( \rho \): Resistivity of the material in ohm-meter (Ω·m)
\( L \): Length of the conductor in meters (m)
\( A \): Cross-sectional area in square meters (m²)

4. Series and Parallel Circuits

Series Circuit Resistance:

Formula:

\( R_{\text{total}} = R_1 + R_2 + \ldots + R_n \)

Description:

Total resistance is the sum of individual resistances.

Parallel Circuit Resistance:

 

Formula:

\( \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots + \frac{1}{R_n} \)

Description:

Total resistance is calculated by the reciprocal of the sum of reciprocals of individual resistances.

5. Electrical Power (P)

Formula:

\( P = VI \)

Alternative Forms:

\( P = I^2R \) and \( P = \frac{V^2}{R} \)

Description:

Power is the rate at which electrical energy is consumed or converted.
\( P \): Power in watts (W)
\( V \): Voltage in volts (V)
\( I \): Current in amperes (A)
\( R \): Resistance in ohms (Ω)

6. Energy Consumption

Formula:

\( E = Pt \)

Description:

Energy consumed by an electrical appliance is the product of power and time.
\( E \): Energy in joules (J) or kilowatt-hours (kWh)
\( P \): Power in watts (W)
\( t \): Time in hours (h) for kWh or seconds (s) for J

7. Electric Potential and Potential Difference

Formula:

\( V = \frac{W}{Q} \)

Description:

Electric potential difference is the work done to move a unit charge between two points.
\( V \): Potential difference in volts (V)
\( W \): Work done in joules (J)
\( Q \): Charge in coulombs (C)

Important Points:

Conductors and Insulators:

Conductors allow easy flow of electric current due to free electrons, while insulators resist the flow.

Factors Affecting Resistance:

Material, length, cross-sectional area, and temperature of the conductor

Ohmic vs Non-Ohmic Conductors:

Ohmic conductors follow Ohm’s Law (constant R), while non-ohmic conductors do not.

SI Units:

Always use standard international (SI) units to ensure accuracy in calculations.

These formulas and points provide a foundational understanding of electricity, crucial for solving numerical problems and understanding the behavior of electric circuits.

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