Resistance in Series and parallel

Resistance in Series and Parallel – Concepts, Formulas & Applications

Resistance is the fundamental component in electrical circuits that opposes the flow of electric current. It plays a key role in converting voltage to current and current to voltage through Ohm’s Law:

$$V = I \times R$$

Where:

• $V$ = Voltage (Volts)

• $I$ = Current (Amperes)

• $R$ = Resistance (Ohms, Ω)

Depending on how resistors are connected in a circuit, their equivalent resistance changes. The two most common connections are Series and Parallel.

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🔹 Resistance in Series

When resistors are connected end-to-end, they form a series circuit.

Formula:

$$R_{eq} = R_1 + R_2 + R_3 + \dots + R_N$$

Key Characteristics:

• Current: Same through all resistors.

• Voltage: Divided across resistors (hence called a voltage divider).

• Equivalent Resistance: Increases as more resistors are added.

👉 Example:
If $R_1 = 10Ω$, $R_2 = 20Ω$, and $R_3 = 30Ω$,

$$R_{eq} = 10 + 20 + 30 = 60Ω$$

Applications:

• Used in voltage divider circuits.

• Simple current limiting in power supply circuits.

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🔹 Resistance in Parallel

When resistors are connected across the same two nodes, they form a parallel circuit.

Formula:

$$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots + \frac{1}{R_N}$$

Key Characteristics:

• Voltage: Same across all resistors.

• Current: Divided among parallel branches (hence called a current divider).

• Equivalent Resistance: Always less than the smallest resistor in the network.

👉 Example:
If $R_1 = 10Ω$, $R_2 = 20Ω$, and $R_3 = 30Ω$,

$$\frac{1}{R_{eq}} = \frac{1}{10} + \frac{1}{20} + \frac{1}{30}$$ $$R_{eq} \approx 5.45Ω$$

Applications:

• Used where low resistance paths are needed.

• Widely applied in household wiring to keep voltage constant across appliances.

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🔹 Conductance in Parallel

In parallel circuits, it’s often easier to use conductance (G) instead of resistance.

$$G = \frac{1}{R}$$

• Units: Siemens (S)

• Equivalent conductance in parallel:

$$G_{eq} = G_1 + G_2 + G_3 + \dots + G_N$$

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✅ Quick Comparison

Feature	Series Circuit	Parallel Circuit
Equivalent Resistance	Sum of resistances (increases)	Less than smallest resistor (decreases)
Current	Same through all resistors	Divided among branches
Voltage	Divided across resistors	Same across each branch
Application	Voltage Divider	Current Divider

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🔗 Related Reads:

• Capacitors in Series and Parallel

• Electrical Power in Series and Parallel

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✅ Disclaimer: The above content is for educational purposes. Always follow electrical safety standards and consult professional guidelines while designing or working on electrical circuits.

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