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Series Circuit Calculator

Calculate total resistance, current, and voltage drops in series electrical circuits with interactive visualization

Parameters

Vⓘ
Enter the total voltage applied to the series circuit

Resistors

Ω
Ω
Ω
Show Trail

Controls

x
Series Circuit Analysis
Animation: Stopped | Time: 0.00s

Calculated Values

Total Resistance:
600.00;Ω600.00;Ω
Circuit Current:
0.02;A0.02;A
Total Power:
0.24;W0.24;W

Voltage Drops:

R1: 2.00V
R2: 4.00V
R3: 6.00V

Examples

Example 1: Three Resistors in Series

A 12V circuit with 100Ω, 200Ω, and 300Ω resistors in series.

  • Total Resistance: 600600
  • Current: 0.020.02
  • Voltage Drops: 2V,4V,6V2V, 4V, 6V

Example 2: Voltage Divider

A 24V circuit with 1kΩ and 2kΩ resistors for voltage division.

  • Total Resistance: 30003000
  • Current: 0.0080.008
  • Voltage Drops: 8V,16V8V, 16V

Example 3: LED Circuit

A 5V circuit with 220Ω resistor and LED (modeled as 2V drop).

  • Total Resistance: 220220
  • Current: 0.01360.0136
  • Voltage Drop: 3V3V

Visualization

Series Circuits

A series circuit is an electrical circuit in which components are connected end-to-end, forming a single path for current flow. In a series circuit, the same current flows through all components, but the voltage is divided among them according to their resistance values.

The total resistance in a series circuit is the sum of all individual resistances: R_total = R₁ + R₂ + R₃ + ... + Rₙ. This is because current must flow through each resistor in sequence, and each resistor adds to the total opposition to current flow.

Current in a series circuit is the same throughout the entire circuit and is calculated using Ohm's Law: I = V_total / R_total. Since there's only one path for current, the current through each component is identical.

Voltage drops across each resistor are proportional to their resistance values: V₁ = I × R₁, V₂ = I × R₂, etc. The sum of all voltage drops equals the total applied voltage: V_total = V₁ + V₂ + V₃ + ... + Vₙ.

Power dissipation in each resistor can be calculated using P = I²R, where I is the current through the resistor and R is its resistance. The total power dissipated equals the sum of power dissipated in all resistors.

Key Concepts

  • Total Resistance: R_total = R₁ + R₂ + R₃ + ... + Rₙ
  • Current: I = V_total / R_total (same throughout circuit)
  • Voltage Drops: V_n = I × R_n (proportional to resistance)
  • Voltage Sum: V_total = V₁ + V₂ + V₃ + ... + Vₙ
  • Power Dissipation: P_n = I² × R_n
  • Single Path: Current flows through all components in sequence

Real-World Applications

  • Voltage Dividers: Creating specific voltage levels from a source
  • LED Circuits: Limiting current through multiple LEDs
  • Sensors: Connecting multiple sensors in series
  • Power Distribution: Understanding voltage drops in long circuits
  • Circuit Protection: Using series resistors for current limiting

Physics Equations

Total Resistance:
Rtotal=R1+R2+R3+⋯+RnR_{total} = R_1 + R_2 + R_3 + \cdots + R_n
Current (Same Everywhere):
I=VtotalRtotalI = \frac{V_{total}}{R_{total}}
Voltage Drop:
Vn=I×RnV_n = I \times R_n
Power Dissipation:
Pn=I2×RnP_n = I^2 \times R_n
Voltage Sum:
Vtotal=V1+V2+V3+⋯+VnV_{total} = V_1 + V_2 + V_3 + \cdots + V_n

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Calculate Total Resistance

Add all resistor values in series:

Equation:

Rtotal=R1+R2+R3+⋯+RnR_{total} = R_1 + R_2 + R_3 + \cdots + R_n

Calculation:

Rtotal=100+200+300=600 ΩR_{total} = 100 + 200 + 300 = 600 \text{ }\Omega

Explanation:

In a series circuit, total resistance is the sum of all individual resistances.

2

Step 2: Calculate Circuit Current

Use Ohm's Law to find current:

Equation:

I=VtotalRtotalI = \frac{V_{total}}{R_{total}}

Calculation:

I=12600=0.0200 AI = \frac{12}{600} = 0.0200 \text{ A}

Explanation:

Current is the same throughout the entire series circuit.

3

Step 3: Calculate Voltage Drops

Find voltage drop across each resistor:

Equation:

Vn=I×RnV_n = I \times R_n

Calculation:

V1=0.0200×100=2.0000 VV2=0.0200×200=4.0000 VV3=0.0200×300=6.0000 VV_1 = 0.0200 \times 100 = 2.0000 \text{ V} \\ V_2 = 0.0200 \times 200 = 4.0000 \text{ V} \\ V_3 = 0.0200 \times 300 = 6.0000 \text{ V}

Explanation:

Voltage drops are proportional to resistance values.

4

Step 4: Verify Voltage Sum

Check that voltage drops sum to total voltage:

Equation:

Vtotal=V1+V2+V3+⋯+VnV_{total} = V_1 + V_2 + V_3 + \cdots + V_n

Calculation:

12=2.0000+4.0000+6.0000=12.0000 V12 = 2.0000 + 4.0000 + 6.0000 = 12.0000 \text{ V}

Explanation:

The sum of all voltage drops must equal the total applied voltage.

Frequently Asked Questions (FAQ)

What is a series circuit?

A series circuit is an electrical circuit where components are connected end-to-end, forming a single path for current flow. The same current flows through all components.

How do I calculate total resistance in series?

Total resistance in series is the sum of all individual resistances: R_total = R₁ + R₂ + R₃ + ... + Rₙ.

Is current the same throughout a series circuit?

Yes, current is the same throughout a series circuit because there's only one path for current flow. Current is calculated as I = V_total / R_total.

How are voltage drops distributed in series?

Voltage drops are proportional to resistance values. Each resistor's voltage drop is V = I × R, and the sum of all voltage drops equals the total applied voltage.

What happens if one component fails in series?

If one component fails (opens), the entire circuit stops working because current cannot flow through the broken path. This is a disadvantage of series circuits.

How do I calculate power dissipation in series?

Power dissipation in each resistor is P = I²R, where I is the current and R is the resistor's value. Total power is the sum of all individual power dissipations.

Practice MCQs

  1. What is the total resistance of 10Ω, 20Ω, and 30Ω resistors in series?
  2. If 12V is applied to a series circuit with 6Ω total resistance, what is the current?
  3. In a series circuit with 2A current, what is the voltage drop across a 5Ω resistor?
  4. What happens to total resistance when you add more resistors in series?
  5. If one resistor in a series circuit burns out, what happens to the current?