PARALLEL CONNECTION OF RESISTORS WORKING MODEL

PARALLEL CONNECTION OF RESISTORS

Absolutely! Let’s delve into the parallel connection of resistors:

**Definition:**
In a parallel connection of resistors, resistors are connected across the same two points, providing multiple paths for the current to flow. Each resistor has the same voltage across its terminals.

**Characteristics:**
1. **Multiple Paths:** In a parallel circuit, there are multiple paths for the flow of current. Each resistor is connected directly across the voltage source, providing a separate path for the current to flow.
2. **Voltage Across Resistor:** Since each resistor is connected directly across the voltage source, they all have the same voltage across their terminals. This voltage is equal to the voltage of the source.
3. **Different Currents:** Unlike in series circuits, where the current remains the same, the current in a parallel circuit is divided among the branches according to the resistance of each branch. The current flowing through each resistor depends on its resistance and Ohm’s Law I = V / R
4. **Additive Conductance:** The total conductance (\(G_total}}) in a parallel circuit is the sum of the conductancesG1, G2, G3, etc.) of each branch. Conductance is the reciprocal of resistance  G = 1/R
5. **Equivalent Resistance:** The total resistance (\(R_total) of resistors in parallel is less than the smallest individual resistance. It can be calculated using the formula for parallel resistance (R_total = 1/R1 + 1/R2 + 1/R3 + …….).

**Applications:**
1. **Voltage Regulation:** Parallel resistor networks are commonly used in voltage regulator circuits to provide a stable output voltage.
2. **Current Sharing:** In power supply circuits, parallel resistors can be used to share the current load among multiple branches, ensuring uniform distribution of current.
3. **Fault Tolerance:** Parallel connections provide redundancy in circuits, ensuring that if one resistor fails, the others can still function.

**Teaching Suggestions:**
– Use circuit diagrams and schematic representations to illustrate parallel connections of resistors.
– Conduct hands-on experiments with resistors connected in parallel to demonstrate the relationship between voltage, current, and resistance.
– Encourage students to calculate total conductance and resistance in parallel circuits using the formulas provided.
– Discuss practical applications of parallel resistor networks in various electronic devices and circuits.

Characteristics:

1. Voltage Drop:
   • The voltage drop across each resistor in parallel is the same and equal to the total voltage applied across the parallel combination.
2. Current Division:
   • The total current entering the parallel combination is divided among the individual resistors based on their resistance values.
   • Resistors with lower resistance values will carry more current than those with higher resistance values.

Application:

• Parallel connection of resistors is commonly used in circuit design to achieve specific voltage and current requirements.
• It allows for customization of resistance values to match the desired operating conditions of the circuit.

Example:

• Consider a circuit with two resistors (�1R1​ and �2R2​) connected in parallel. If a voltage $V$ is applied across the parallel combination, the current flowing through each resistor can be calculated using Ohm’s Law, and the equivalent resistance �eqReq​ can be determined using the reciprocal formula.

Conclusion:

Parallel connection of resistors provides flexibility in circuit design by allowing customization of resistance values and current distribution. By understanding the principles and characteristics of parallel connection, engineers can design circuits with desired performance and functionality.