This chapter discusses the concept of electric current, its laws, and the behavior of currents in various materials, particularly in conductors.
CURRENT ELECTRICITY – Formula & Equation Sheet
Essential formulas and equations from Physics Part - I, tailored for Class 12 in Physics.
This one-pager compiles key formulas and equations from the CURRENT ELECTRICITY chapter of Physics Part - I. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
I = \frac{Q}{t}
I represents electric current (in amperes), Q is the charge (in coulombs), and t is time (in seconds). This formula defines current as the rate at which charge flows through a conductor.
V = IR
V is voltage (in volts), I is current (in amperes), and R is resistance (in ohms). Ohm's Law establishes the relationship between voltage, current, and resistance.
R = \rho \frac{l}{A}
R is the resistance (in ohms), \rho is resistivity (in ohm-meters), l is the length of the conductor (in meters), and A is the cross-sectional area (in square meters). This formula shows how resistance depends on material properties and dimensions.
P = IV
P is power (in watts), I is current (in amperes), and V is voltage (in volts). This formula expresses the electrical power consumed in a circuit.
P = I^2R
P is power (in watts), I is current (in amperes), and R is resistance (in ohms). This form is used to compute power loss due to resistance in a conductor.
E = j \rho
E is the electric field (in volts per meter), j is the current density (in amperes per square meter), and \rho is resistivity (in ohm-meters). This relates the electric field to current density through resistivity.
j = \frac{I}{A}
j is the current density (in amperes per square meter), I is the current (in amperes), and A is the area (in square meters). This defines how current is distributed over a cross-sectional area.
\varepsilon = V + Ir
\varepsilon is the electromotive force (emf) of the cell (in volts), V is the terminal voltage (in volts), and r is internal resistance (in ohms). This formula accounts for voltage drop across internal resistance.
\rho_T = \rho_0 [1 + \alpha (T - T_0)]
\rho_T is the resistivity at temperature T, \rho_0 is the resistivity at reference temperature T0, and \alpha is the temperature coefficient of resistivity. This shows how resistivity changes with temperature.
\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}
This formula gives the equivalent resistance (R_eq) for resistors R_1 and R_2 in parallel. It helps to find total resistance in the parallel circuit.
Equations
V_A - V_B = IR
This equation states that the potential difference across components in a circuit is equal to the product of the current (I) flowing through the component and its resistance (R).
E = V + Ir
For a cell in a circuit, this equation relates the electromotive force (E) to the terminal voltage (V) and the current (I) multiplied by the internal resistance (r).
R_L = \frac{V_T}{I}
R_L represents the load resistance across which the terminal voltage (V_T) appears due to the current (I) flowing through it.
V = E - Ir
This relates the terminal voltage (V) to the electromotive force (E) and the voltage drop across the internal resistance (Ir) of the source.
j = \sigma E
j is current density, \sigma is the conductivity, and E is the electric field. This states that current density is proportional to the electric field.
R = \frac{\rho l}{A}
This equation shows the relationship between resistance (R), resistivity (\rho), the length of the conductor (l), and its cross-sectional area (A).
I = n q v_d A
This represents the relationship of current (I) with the number density of charge carriers (n), the charge of each carrier (q), drift velocity (v_d), and the cross-sectional area (A) of the conductor.
P = VI = I^2R = \frac{V^2}{R}
This shows different ways to express the power (P) in a circuit based on voltage (V) and current (I).
V = IR + \varepsilon
This equation indicates that the voltage (V) across an electric component is the sum of the current times resistance and the emf.
E = j \rho
This relates the electric field (E) to the current density (j) and the resistivity (\rho) of the material.
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