Electrical Power and Resistors in Circuits
Electrical Power in Resistors
Definition
Power
Power is the rate at which energy is transferred or converted.
In electrical circuits, power is dissipated aspower is dissipated as thermal energy in resistors.
The formula for power in a resistor is:$$
P = IV
$$ where:
- P is the power (in watts, W)
- I is the current (in amperes, A)
- V is the potential difference (in volts, V)
Using Ohm’s Law ($V = IR$), we can express power in two other forms:
- In terms of current and resistance:$$
P = I^2R
$$ - In terms of voltage and resistance:$$
P = \frac{V^2}{R}
$$
Choose the power formula that matches the information you have.
- If you know the current and resistance, use $P = I^2R$.
- If you know the voltage and resistance, use $P = \frac{V^2}{R}$.
Example question
A resistor has a resistance of 5 Ω and a current of 2 A flowing through it. Calculate the power dissipated.
Solution
Using $P = I^2R$:
$$
P = (2 \, \mathrm{A})^2 \times 5 \, \Omega = 20 \, \mathrm{W}
$$
Resistors in Series Circuits
Definition
Series circuit
In a series circuit, resistors are connected end-to-end, forming a single path for current.
Key Characteristics of Series Circuits
- Current: The current is the same through all resistors. $$
I = I_1 = I_2 = I_3 = \ldots
$$ - Voltage: The total voltage across the circuit is the sum of the voltages across each resistor. $$
V = V_1 + V_2 + V_3 + \ldots
$$ - Resistance: The total resistance is the sum of the individual resistances. $$
R_s = R_1 + R_2 + R_3 + \ldots
$$
In series circuits, adding more resistors increases the total resistance, which decreases the current for a given voltage.
