Physics Formula Electricity

Physics Formulas for Electricity

Electricity is a fundamental concept in physics, involving the presence and flow of electric charge. Understanding electricity involves various formulas that describe how electric charges interact and behave. Here are some essential electricity formulas along with examples to illustrate their application.

1. Ohm's Law

Ohm's Law is one of the most basic and important laws in electricity. It states the relationship between voltage (V), current (I), and resistance (R):

\[ V = I \cdot R \]

Example:

If a current of 2 A flows through a resistor of 5 Ω, the voltage across the resistor is:

\[ V = I \cdot R = 2 \, \text{A} \times 5 \, \text{Ω} = 10 \, \text{V} \]

2. Power in Electrical Circuits

Electrical power (P) can be calculated using the voltage and current in a circuit. The formula is:

\[ P = V \cdot I \]

Alternatively, using Ohm's Law, power can also be expressed as:

\[ P = I^2 \cdot R \]

or

\[ P = \frac{V^2}{R} \]

Example:

If a device operates at 12 V and draws a current of 3 A, the power consumed is:

\[ P = V \cdot I = 12 \, \text{V} \times 3 \, \text{A} = 36 \, \text{W} \]

3. Kirchhoff's Laws

Kirchhoff's Current Law (KCL)

KCL states that the total current entering a junction equals the total current leaving the junction:

\[ \sum I_{\text{in}} = \sum I_{\text{out}} \]

Example:

If three currents, 2 A, 3 A, and 5 A, enter a junction, and two currents, 4 A and 6 A, leave the junction, KCL ensures the sum of currents entering and leaving are equal:

\[ 2 \, \text{A} + 3 \, \text{A} + 5 \, \text{A} = 4 \, \text{A} + 6 \, \text{A} \]

\[ 10 \, \text{A} = 10 \, \text{A} \]

Kirchhoff's Voltage Law (KVL)

KVL states that the sum of all voltages around a closed loop in a circuit is zero:

\[ \sum V = 0 \]

Example:

In a closed loop with three components having voltages of 5 V, -2 V, and -3 V:

\[ 5 \, \text{V} + (-2 \, \text{V}) + (-3 \, \text{V}) = 0 \]

4. Coulomb's Law

Coulomb's Law describes the electrostatic force (F) between two charges (q1 and q2) separated by a distance (r):

\[ F = k_e \frac{q_1 q_2}{r^2} \]

where \( k_e \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{N m}^2 \text{C}^{-2} \)).

Example:

If two charges, \( q_1 = 1 \, \text{C} \) and \( q_2 = 2 \, \text{C} \), are 1 m apart, the force between them is:

\[ F = 8.99 \times 10^9 \frac{(1 \, \text{C}) (2 \, \text{C})}{(1 \, \text{m})^2} = 17.98 \times 10^9 \, \text{N} \]

5. Electric Field

The electric field (E) due to a point charge (q) at a distance (r) is given by:

\[ E = k_e \frac{q}{r^2} \]

Example:

If a charge of 1 C is placed 1 m away, the electric field at that point is:

\[ E = 8.99 \times 10^9 \frac{1 \, \text{C}}{(1 \, \text{m})^2} = 8.99 \times 10^9 \, \text{N/C} \]

6. Capacitance

The capacitance (C) of a capacitor is defined as the ratio of the charge (Q) on each conductor to the potential difference (V) between them:

\[ C = \frac{Q}{V} \]

The unit of capacitance is the Farad (F).

Example:

If a capacitor holds a charge of 3 C with a voltage of 6 V across it, the capacitance is:

\[ C = \frac{3 \, \text{C}}{6 \, \text{V}} = 0.5 \, \text{F} \]

7. Energy Stored in a Capacitor

The energy (E) stored in a capacitor is given by:

\[ E = \frac{1}{2} C V^2 \]

Example:

For a capacitor with a capacitance of 2 F and a voltage of 5 V, the energy stored is:

\[ E = \frac{1}{2} \times 2 \, \text{F} \times (5 \, \text{V})^2 = \frac{1}{2} \times 2 \times 25 = 25 \, \text{J} \]

These fundamental formulas provide a solid understanding of electricity and its principles, which are crucial for further studies in physics and engineering.

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