Section 4.3: Resistors
Resistors are components that oppose the flow of electric current. They are fundamental in controlling current and dividing voltage in circuits.
- Series Resistors: Total resistance is the sum: \[ R_\text{total} = R_1 + R_2 + \dots + R_n \]
- Parallel Resistors: Total resistance is found via: \[ \frac{1}{R_\text{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n} \]
- Power Dissipation: Resistors convert electrical energy into heat: \[ P = I^2 R = V^2 / R = IV \]
- Color Codes: Resistors often use colored bands to indicate resistance values.
Example: Series and Parallel Resistors
Find the total resistance of two resistors R1 = 4 Ω and R2 = 6 Ω connected (a) in series, (b) in parallel.
(a) Series: \( R_\text{total} = R_1 + R_2 = 4 + 6 = 10 \, \Omega \)
(b) Parallel: \( \frac{1}{R_\text{total}} = \frac{1}{4} + \frac{1}{6} = \frac{5}{12} \Rightarrow R_\text{total} = \frac{12}{5} = 2.4 \, \Omega \)
Practice Problems
- Three resistors 2 Ω, 3 Ω, and 6 Ω are in series. Calculate the total resistance.
- Three resistors 2 Ω, 3 Ω, and 6 Ω are in parallel. Find the total resistance.
- A series circuit has resistors 5 Ω and 10 Ω with a 15 V battery. Calculate the current and voltage drop across each resistor.
- A 12 Ω resistor carries 2 A. Calculate the power dissipated.
- Explain how combining series and parallel resistors can adjust total resistance in practical circuits.