Series and Parallel Circuits
I. Series Circuits
1. Ohm’s Law:
- Statement: The current flowing through a conductor is directly proportional to the voltage applied across its ends and inversely proportional to the resistance of the conductor.
- Formula: I = U/R
- I: Current (A)
- U: Voltage (V)
- R: Resistance (Ω)
2. Characteristics of Current and Voltage in a Series Circuit:
- Current: The current at every point in a series circuit is the same.
- I = I1 = I2 = …
- Voltage: The voltage across the entire circuit is equal to the sum of the voltages across each individual resistor.
- U = U1 + U2 + …
3. Relationship between Voltage and Resistance in a Series Circuit:
- The voltage across each resistor is directly proportional to its resistance.
- U1/U2 = R1/R2
4. Equivalent Resistance of a Series Circuit:
- Definition: The equivalent resistance of a series circuit is the resistance that can replace the entire circuit such that, with the same voltage applied, the current flowing through the circuit remains unchanged.
- Formula: Rtđ = R1 + R2 + …
- Note:
- The equivalent resistance of a series circuit is always greater than the resistance of each individual component.
- Rtđ = R1 + R2 if the circuit only has 2 resistors.
II. Parallel Circuits
1. Characteristics of Current and Voltage in a Parallel Circuit:
- Current: The current flowing through the main circuit is equal to the sum of the currents flowing through each branch.
- I = I1 + I2 + …
- Voltage: The voltage across the entire parallel circuit is equal to the voltage across each individual resistor.
- U = U1 = U2 = …
2. Relationship between Current and Resistance in a Parallel Circuit:
- The current flowing through each resistor is inversely proportional to its resistance.
- I1/I2 = R2/R1
3. Equivalent Resistance of a Parallel Circuit:
- Definition: The equivalent resistance of a parallel circuit is the resistance that can replace the entire circuit such that, with the same voltage applied, the current flowing through the circuit remains unchanged.
- Formula: 1/Rtđ = 1/R1 + 1/R2 + …
- Note:
- The equivalent resistance of a parallel circuit is always smaller than the resistance of each individual component.
- Rtđ = (R1×R2)/(R1+R2) if the circuit only has 2 resistors.
III. General Notes:
- The formulas for calculating equivalent resistance and the relationships between current, voltage, and resistance in series and parallel circuits only apply to simple circuits that do not contain other components like capacitors, inductors, etc.
- When solving circuit problems, it is important to consider factors such as: the type of circuit, the number and value of resistors, the given voltage or current, etc., to choose the appropriate formula.
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