TOPICS
Keywords
- Electricity
- Resistors
- Parallel
- Equivalent Resistance
- Voltage Difference (DDP)
- Current Intensity
- Ohm's Law
- Parallel Circuit
Key Questions
- How to calculate the equivalent resistance in a parallel resistor circuit?
- How does the voltage difference (DDP) affect each resistor in a parallel circuit?
- What is the relationship between the total current and the currents in the branches of a parallel circuit?
Crucial Topics
- Each resistor in a parallel circuit has the same voltage difference (voltage) as the source.
- The total current is the sum of the currents through each parallel resistor.
- The equivalent resistance in a parallel circuit is always less than the resistance of any of the individual resistors.
Fundamental Formulas
- Ohm's Law:
V = I * R
- Calculation of Equivalent Resistance in Parallel:
1/Req = 1/R1 + 1/R2 + ... + 1/Rn
- Total Current in the Circuit:
Itotal = I1 + I2 + ... + In
- Voltage Difference in Parallel Resistors:
Vtotal = V1 = V2 = ... = Vn
NOTES
Key Terms
- Electricity: Phenomenon associated with the presence and flow of electric charge.
- Resistors: Components that offer resistance to the passage of electric current, converting electrical energy into heat.
- Parallel: Circuit configuration where two or more components are connected in multiple current paths.
- Equivalent Resistance (Req): Represents the total resistance of a circuit, replacing all resistors with a single resistor with equivalent resistance.
- Voltage Difference (DDP): Also known as voltage, it is the electrical potential energy per unit of charge that drives the electric current.
- Current Intensity: Amount of electric charge that passes through a point in the circuit in one second, measured in amperes.
- Ohm's Law: Relationship between voltage (V), current (I), and resistance (R) in a circuit, expressed by the formula
V = I * R
. - Parallel Circuit: Type of circuit where the components are connected so that the voltage is the same across all of them.
Main Ideas and Concepts
- The voltage across all resistors in parallel is identical, equal to the voltage from the power source.
- Total Current: The value of the total current flowing through a parallel circuit is the sum of the currents flowing through each independent path.
- Importance of equivalent resistance: While the total resistance decreases, the total current in the circuit increases, illustrating an inverse characteristic of the resistance-current relationship.
Topic Contents
- Equivalent Resistance in Parallel: To calculate the equivalent resistance, we add the inverses of the individual resistances and take the inverse of the result.
- Practical example: If R1 = 100Ω and R2 = 200Ω, then
1/Req = 1/100 + 1/200
, or1/Req = 0.01 + 0.005 = 0.015
. Therefore,Req = 1/0.015 ≈ 66.67Ω
.
- Practical example: If R1 = 100Ω and R2 = 200Ω, then
- Ohm's Law in Parallel Circuit: Applying
V = I * R
for each resistor, the same voltage will result in different currents depending on the individual resistance. - Current Distribution: The current entering a node (connection point in a circuit) is equal to the current leaving the node, according to Kirchhoff's first law, or the node law.
Examples and Cases
- Current Calculation Example: Given a 10V voltage source connected to two resistors in parallel, R1 = 2Ω and R2 = 5Ω, we calculate the total current.
- Current in R1:
I1 = V/R1 = 10V/2Ω = 5A
- Current in R2:
I2 = V/R2 = 10V/5Ω = 2A
- Total Current:
I_total = I1 + I2 = 5A + 2A = 7A
- Current in R1:
- DDP Example in Parallel: Two resistors, R1 and R2, are in parallel with a DDP of 9V from the source. Both resistors are subject to this same voltage, regardless of their resistance values.
SUMMARY
Summary of the most relevant points
- The Voltage Difference (DDP) is constant across all resistors in a parallel circuit, equal to the voltage supplied by the source.
- The Equivalent Resistance (Req) in a parallel circuit is calculated by summing the inverses of the individual resistances:
1/Req = 1/R1 + 1/R2 + ... + 1/Rn
. - In a parallel circuit, the Total Current (Itotal) is equal to the sum of the currents in each individual path:
Itotal = I1 + I2 + ... + In
. - Ohm's Law serves as the basis for understanding how voltage relates to current and resistance in each part of the circuit.
Conclusions
- Understanding of Parallel Circuits: The equivalent resistance in a parallel circuit will always be less than the smallest of the circuit's resistances.
- Current and Voltage Analysis: It is understood that the voltage is the same across each resistor, while the currents vary according to individual resistances.
- Problem Solving: The calculation of equivalent resistance and Ohm's Law are applied to solve problems involving resistors in parallel.
- Inverse Relationship: The inverse relationship between equivalent resistance and total current in the circuit is recognized – the lower the equivalent resistance, the greater the current flowing in the circuit.