1 Answer
Here are the key formulas related to resistance and resistivity:
1. Formula for Resistance (R):
The resistance of a conductor (like a wire) is given by the formula:
\[
R = \rho \times \frac{L}{A}
\]
Where:
This formula shows how resistance depends on the material (through resistivity), the length, and the area of the conductor.
2. Resistivity (ρ):
Resistivity is a property of the material that tells you how strongly it resists the flow of electric current. It's a constant for a given material.
It’s calculated from the above formula:
\[
\rho = R \times \frac{A}{L}
\]
Where:
3. Ohm’s Law:
Ohm’s Law relates voltage (V), current (I), and resistance (R):
\[
V = I \times R
\]
Where:
4. Temperature Dependence of Resistance:
The resistance of most materials changes with temperature. For metals, resistance increases as temperature increases, while for semiconductors, it generally decreases.
The formula for resistance at a new temperature is:
\[
R_T = R_0 \left( 1 + \alpha (T - T_0) \right)
\]
Where:
5. Resistance of a Parallel Combination:
When resistors are connected in parallel, the total resistance is found using the formula:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}
\]
Where:
6. Resistor in Series:
When resistors are connected in series, the total resistance is simply the sum of the individual resistances:
\[
R_{\text{total}} = R_1 + R_2 + \cdots + R_n
\]
Where:
These are the key formulas you’ll often use for problems involving resistance and resistivity.
1. Formula for Resistance (R):
The resistance of a conductor (like a wire) is given by the formula:
\[
R = \rho \times \frac{L}{A}
\]
Where:
- R = Resistance (measured in ohms, Ω)
- ρ (rho) = Resistivity of the material (measured in ohm-meter, Ω·m)
- L = Length of the conductor (measured in meters, m)
- A = Cross-sectional area of the conductor (measured in square meters, m²)
This formula shows how resistance depends on the material (through resistivity), the length, and the area of the conductor.
2. Resistivity (ρ):
Resistivity is a property of the material that tells you how strongly it resists the flow of electric current. It's a constant for a given material.
It’s calculated from the above formula:
\[
\rho = R \times \frac{A}{L}
\]
Where:
- ρ = Resistivity (measured in Ω·m)
- R = Resistance (measured in ohms, Ω)
- A = Cross-sectional area (measured in square meters, m²)
- L = Length (measured in meters, m)
3. Ohm’s Law:
Ohm’s Law relates voltage (V), current (I), and resistance (R):
\[
V = I \times R
\]
Where:
- V = Voltage (measured in volts, V)
- I = Current (measured in amperes, A)
- R = Resistance (measured in ohms, Ω)
4. Temperature Dependence of Resistance:
The resistance of most materials changes with temperature. For metals, resistance increases as temperature increases, while for semiconductors, it generally decreases.
The formula for resistance at a new temperature is:
\[
R_T = R_0 \left( 1 + \alpha (T - T_0) \right)
\]
Where:
- R_T = Resistance at temperature T (measured in ohms, Ω)
- R_0 = Resistance at reference temperature T₀ (measured in ohms, Ω)
- α = Temperature coefficient of resistance (measured in 1/°C)
- T = New temperature (measured in °C)
- T₀ = Reference temperature (measured in °C)
5. Resistance of a Parallel Combination:
When resistors are connected in parallel, the total resistance is found using the formula:
\[
\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}
\]
Where:
- R_total = Total resistance (measured in ohms, Ω)
- R₁, R₂, ..., Rn = Individual resistances (measured in ohms, Ω)
6. Resistor in Series:
When resistors are connected in series, the total resistance is simply the sum of the individual resistances:
\[
R_{\text{total}} = R_1 + R_2 + \cdots + R_n
\]
Where:
- R_total = Total resistance (measured in ohms, Ω)
- R₁, R₂, ..., Rn = Individual resistances (measured in ohms, Ω)
These are the key formulas you’ll often use for problems involving resistance and resistivity.