resistor

Resistor Calculator

Ohm's law & circuit analysis • 2026 standards

Resistor Formulas:

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\( \text{Ohm's Law: } V = I \times R \)

\( \text{Power: } P = V \times I = I^2 \times R = \frac{V^2}{R} \)

\( \text{Series: } R_T = R_1 + R_2 + R_3 + \ldots \)

\( \text{Parallel: } \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots \)

\( \text{Voltage Divider: } V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2} \)

These formulas calculate electrical properties in circuits. Ohm's law relates voltage, current, and resistance. Power formulas determine energy dissipation. Series and parallel calculations find equivalent resistance.

Example: For a 12V circuit with 4Ω resistor:

Current: I = V/R = 12/4 = 3A

Power: P = V×I = 12×3 = 36W

For two 4Ω resistors in series: RT = 4+4 = 8Ω

For two 4Ω resistors in parallel: 1/RT = 1/4+1/4 = 1/2, so RT = 2Ω

Circuit Specifications

Advanced Options

Results

4.00 Ω
Resistance
3.00 A
Current
12.00 V
Voltage
36.00 W
Power
Temperature Coefficient
±100 ppm/°C
Tolerance
±5%
Power Rating
50W
Configuration
Series

Ohm's Law Fundamentals

What is Ohm's Law?

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points. It's expressed as V = I × R, where V is voltage, I is current, and R is resistance.

Ohm's Law Variations

Derived formulas from Ohm's Law:

  • V = I × R (voltage = current × resistance)
  • I = V ÷ R (current = voltage ÷ resistance)
  • R = V ÷ I (resistance = voltage ÷ current)
  • P = V × I (power = voltage × current)
Key Rules:
  • Voltage is measured in volts (V)
  • Current is measured in amperes (A)
  • Resistance is measured in ohms (Ω)
  • Power is measured in watts (W)
  • Applies to linear resistive elements

Circuit Configurations

Series vs Parallel

In series circuits, resistors are connected end-to-end, while in parallel circuits, resistors are connected across the same two points. Each configuration affects total resistance differently.

Configuration Formulas

Series and parallel calculations:

  1. Series: RT = R1 + R2 + ... + Rn
  2. Parallel: 1/RT = 1/R1 + 1/R2 + ... + 1/Rn
  3. Two resistors in parallel: RT = (R1 × R2) ÷ (R1 + R2)
  4. Voltage divider: Vout = Vin × (R2 ÷ (R1 + R2))
Configuration Guidelines:
  • Series: Total R increases
  • Parallel: Total R decreases
  • Series: Current same in all
  • Parallel: Voltage same across all

Electrical Engineering Learning Quiz

Question 1: Multiple Choice - Ohm's Law

According to Ohm's Law, if the voltage across a resistor is doubled while the resistance remains constant, what happens to the current?

Solution:

The correct answer is C) Current doubles. From Ohm's Law: I = V/R. If voltage doubles (V becomes 2V) and resistance stays the same, then I = 2V/R = 2 × (V/R) = 2 × original current.

Pedagogical Explanation:

This demonstrates the direct proportionality between voltage and current in Ohm's Law. When voltage increases by a factor, current increases by the same factor, assuming resistance remains constant.

Key Definitions:

Ohm's Law: V = I × R, relating voltage, current, and resistance

Direct Proportionality: When one variable increases, the other increases by the same factor

Constant Resistance: Fixed opposition to current flow

Important Rules:

• I = V/R (current equals voltage divided by resistance)

• Direct relationship: V ↑ → I ↑

• Assumes linear behavior

Tips & Tricks:

• Remember: I = V/R

• If V doubles, I doubles (same R)

• If R doubles, I halves (same V)

Common Mistakes:

• Confusing direct and inverse relationships

• Forgetting to keep resistance constant

• Not understanding proportional relationships

Question 2: Series Resistance Calculation

Calculate the total resistance of three resistors connected in series: 10Ω, 20Ω, and 30Ω.

Solution:

Step 1: Apply the series resistance formula

RT = R1 + R2 + R3

Step 2: Substitute values

RT = 10Ω + 20Ω + 30Ω

Step 3: Calculate

RT = 60Ω

The total resistance is 60 ohms.

Pedagogical Explanation:

In series circuits, total resistance is the sum of individual resistances. This occurs because current must pass through each resistor sequentially, experiencing the full resistance of each element.

Key Definitions:

Series Circuit: Components connected end-to-end forming single path

Total Resistance: Combined opposition to current flow

Sequential Flow: Current passes through each component

Important Rules:

• Series: RT = R1 + R2 + R3 + ...

• Current is same in all resistors

• Voltage divides among resistors

Tips & Tricks:

• Always add resistances in series

• Total resistance > any individual resistor

• Same current through all components

Common Mistakes:

• Using parallel formula for series

• Forgetting to add all resistors

• Confusing with parallel connections

Question 3: Word Problem - Parallel Resistance

Calculate the total resistance of two resistors connected in parallel: 10Ω and 15Ω. Use the formula: 1/RT = 1/R1 + 1/R2.

Solution:

Step 1: Apply the parallel resistance formula

1/RT = 1/R1 + 1/R2

Step 2: Substitute values

1/RT = 1/10 + 1/15

Step 3: Find common denominator

1/RT = 3/30 + 2/30 = 5/30

Step 4: Solve for RT

RT = 30/5 = 6Ω

The total resistance is 6 ohms.

Pedagogical Explanation:

In parallel circuits, total resistance is always less than the smallest individual resistor. This occurs because current has multiple paths to flow, effectively reducing the overall opposition to current flow.

Key Definitions:

Parallel Circuit: Components connected across same two points

Multiple Paths: Current can flow through different routes

Reduced Resistance: Overall opposition decreases

Important Rules:

• Parallel: 1/RT = 1/R1 + 1/R2 + ...

• Total resistance < smallest resistor

• Voltage is same across all resistors

Tips & Tricks:

• For two resistors: RT = (R1×R2)/(R1+R2)

• Total resistance is always smaller

• Same voltage across all branches

Common Mistakes:

• Adding resistances directly in parallel

• Forgetting to take reciprocal

• Using series formula for parallel

Question 4: Application-Based Problem - Power Calculation

Calculate the power dissipated by a 12Ω resistor with 24V across it. Use the formula: P = V²/R.

Solution:

Step 1: Apply the power formula

P = V²/R

Step 2: Substitute values

P = (24)²/12

Step 3: Calculate

P = 576/12 = 48W

The resistor dissipates 48 watts of power.

Pedagogical Explanation:

This calculation shows how electrical energy is converted to heat in a resistor. Power dissipation is critical for selecting appropriate resistor ratings to prevent overheating and failure.

Key Definitions:

Power Dissipation: Energy converted to heat in resistor

Heat Generation: Thermal energy produced by current flow

Power Rating: Maximum safe power for component

Important Rules:

• P = V²/R = I²R = VI

• Power is always positive

• Resistors convert electrical to thermal energy

Tips & Tricks:

• Use P = V²/R when voltage is known

• Use P = I²R when current is known

• Always check power ratings

Common Mistakes:

• Forgetting to square voltage

• Using wrong formula variant

• Not considering power ratings

Question 5: Multiple Choice - Voltage Divider

In a voltage divider circuit with R1 = 10Ω and R2 = 20Ω, and input voltage of 30V, what is the output voltage across R2?

Solution:

The correct answer is C) 20V. Using the voltage divider formula: Vout = Vin × (R2/(R1+R2)). Substituting values: Vout = 30 × (20/(10+20)) = 30 × (20/30) = 30 × (2/3) = 20V.

Pedagogical Explanation:

A voltage divider splits input voltage proportionally based on resistor values. The output voltage is the fraction of input voltage equal to the ratio of the lower resistor to the total resistance.

Key Definitions:

Voltage Divider: Circuit that divides input voltage

Proportional Split: Voltage distributed based on resistance

Series Resistors: Resistors connected end-to-end

Important Rules:

• Vout = Vin × (R2/(R1+R2))

• Output is always less than input

• Proportional to resistor ratio

Tips & Tricks:

• Output is always less than input

• Higher R2 = higher output

• Use for signal level adjustment

Common Mistakes:

• Using wrong resistor in numerator

• Forgetting to add resistors in denominator

• Not understanding the proportional relationship

Resistor Calculator

FAQ

Q: What's the difference between series and parallel resistor connections?

A: The main differences are:

  • Series: Resistors connected end-to-end
  • Parallel: Resistors connected across same points

Mathematically:

Series: RT = R1 + R2 + ... (resistance increases)

Parallel: 1/RT = 1/R1 + 1/R2 + ... (resistance decreases)

In series, current is the same through all resistors, but voltage divides. In parallel, voltage is the same across all resistors, but current divides.

Q: How do I read resistor color codes?

A: The 4-band color code system:

  • Band 1: First digit
  • Band 2: Second digit
  • Band 3: Multiplier (number of zeros)
  • Band 4: Tolerance (accuracy)

For example, Brown-Black-Red-Gold:

Brown = 1, Black = 0, Red = ×100, Gold = ±5%

Result: 10 × 100 = 1,000Ω ±5%

Common colors: Black(0), Brown(1), Red(2), Orange(3), Yellow(4), Green(5), Blue(6), Violet(7), Gray(8), White(9)

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This calculator was created by our General & Utility Calculators Team , may make errors. Consider checking important information. Updated: April 2026.