Class 12 Physics Current Electricity Formulas

• It is the rate of flow of charge per unit time through the conductor (wire).

  $$I(t)\equiv \underset{\mathrm{\Delta }t\to 0}{\lim }\frac{\mathrm{\Delta }Q}{\mathrm{\Delta }t}$$

It states that the potential difference across the terminals of the conductor will be directly proportional to the current.

$$\mathrm{ \; \; V}\propto I\text{<br>}$$

$$V=RI$$

Resistance: A property of a conductors that oppose the flow of charge.

• $$R=\frac{V}{I}$$
• $$R=\rho \frac{L}{A}$$

Ohm's Law with properties of a wire

$$V=I\times R=I\times \rho \frac{L}{A}$$

Current Density: It measures current per unit cross-sectional area of the wire.

$$\mathbf{j}=\; I/A\; =\sigma \mathbf{E }$$

Conductivity: It is the measure of the ability to conduct electric current through the wire.

$$\sigma =\frac{1}{\rho }$$

Related useful formulas

• $$\mathbf{E}=\rho \mathbf{j}\text{<br>}$$
• $$\mathbf{j}=\sigma \mathbf{E}\text{<br>}$$

• Acceleration on Electrons (When an Electric Field (E) is applied)

$$a_{}=\; --\frac{e\mathrm{<br>}E}{m}$$

• Drift Velocity

$$v_d=\frac{e\tau E}{m}$$

• Amount of charges passing through a wire in time Δt (cross-sectional area A)

• Current passing in Δt  time

• Current Density (through the wire)

$$\mathbf{j\; =\; nev}=\frac{n{e}^2\tau }{m}\mathbf{E}$$

• Conductivity Formula (For properties of wire)

$$\sigma =\frac{n{e}^2\tau }{m}$$

• Mobility: Drift velocity for per unit electric field applied

$$\mu =\frac{v_d}{E}=\frac{e\tau }{m}$$

Resistance and resistivity are directly proportional to temperature. It means an increase in temperature will increase both of these and reduce conductivity ( since it is reciprocal of resistance).

• Effect of Temperature on Resistivity

• Effect of Temperature on Resistance

$$R_T=R_0[1+\alpha (T-T_0)]$$

• Effect of Temperature on Conductivity

We know, 

$$\sigma = \frac{1}{\rho}$$

So, 

$$\sigma_T = \frac{1}{\rho_T} = \frac{1}{\rho_0 [1 + \alpha (T - T_0)]}$$

If  change in temperature is small,

$${\sigma }_T\approx {\sigma }_0[1-\alpha (T-T_0)]$$

• Energy in t time:

$$E = V I t = I^2 R t = \frac{V^2 t}{R}$$

• Power

$$P=IV=I^{2}R=\frac{V^2}{R}$$

• Electromotive Force

ε = Open-circuit voltage of the cell when no current flows

• Actual Terminal Voltage

$$\text{V}=\epsilon -Ir$$

• Current in the Circuit

$$I=\frac{\epsilon }{R+r}$$

• Combination of Cells

• Junction Rule: The sum of all currents entering a junction = the sum of currents leaving the junction.

$$\sum I_{\text{in}}=\sum I_{\text{out}}$$

• Loop Rule: The algebraic sum of changes in potentials in a closed loop is zero.

$$\sum \mathrm{\Delta }V=\mathrm{0 \; (In\; a\; closed\; loop)}$$

• When the measure of current in the galvanometer is zero.

  $$\frac{P}{Q}=\frac{R}{S}$$