Section 4.1: DC Circuits
DC circuits are electrical circuits powered by a constant direct current (DC) source, such as a battery. This section introduces basic components and principles in DC circuits.
- Current (I): Flow of electric charge through a conductor, measured in amperes (A).
- Voltage (V): Electric potential difference between two points, measured in volts (V).
- Resistance (R): Opposition to the flow of current, measured in ohms (Ω).
- Ohm’s Law: Relationship between voltage, current, and resistance: \[ V = I \cdot R \]
- Series Circuits: Components connected end-to-end; same current flows through all components.
- Parallel Circuits: Components connected across the same voltage; current divides among branches.
Example: Current in a Series Circuit
A 12 V battery is connected to two resistors in series: R1 = 4 Ω, R2 = 6 Ω. Find the current in the circuit.
Total resistance: \( R_\text{total} = R_1 + R_2 = 4 + 6 = 10 \, \Omega \)
Current: \( I = \frac{V}{R_\text{total}} = \frac{12}{10} = 1.2 \, \text{A} \)
Practice Problems
- A 9 V battery is connected to a resistor of 3 Ω. Calculate the current through the resistor.
- Two resistors, 5 Ω and 10 Ω, are connected in series across a 15 V battery. Find the current and voltage drop across each resistor.
- Three resistors, 6 Ω, 3 Ω, and 2 Ω, are connected in parallel across a 12 V battery. Determine the current through each resistor.
- Explain the difference between series and parallel circuits in terms of current and voltage.
- A circuit has two resistors, 4 Ω and 6 Ω, in series with a 12 V battery. Calculate the power dissipated in each resistor.