Parallel Circuit Calculator
Use this calculator to determine the total equivalent resistance and total current in a parallel circuit. Enter the resistance values for up to four resistors and the voltage of the power source (optional, for current calculation).
Results:
Total Equivalent Resistance:
Total Current:
Understanding Parallel Circuits
A parallel circuit is a type of electrical circuit where components are connected across the same two points, providing multiple paths for the current to flow. This configuration has distinct characteristics compared to a series circuit, particularly regarding resistance, voltage, and current.
Key Characteristics of Parallel Circuits:
- Voltage: The voltage across each component in a parallel circuit is the same. If you have a 12V battery, every resistor connected in parallel to that battery will have 12V across it.
- Current: The total current flowing from the source is divided among the parallel branches. The sum of the currents through each branch equals the total current supplied by the source (Kirchhoff's Current Law).
- Resistance: Adding more resistors in parallel actually decreases the total equivalent resistance of the circuit. This is because adding more paths for current to flow makes it "easier" for the total current to pass through the circuit.
Formulas for Parallel Circuits:
1. Total Equivalent Resistance (Rt):
The reciprocal of the total equivalent resistance is equal to the sum of the reciprocals of the individual resistances:
1 / Rt = 1 / R1 + 1 / R2 + 1 / R3 + ...
Therefore, to find Rt:
Rt = 1 / (1 / R1 + 1 / R2 + 1 / R3 + ...)
2. Total Current (It):
Using Ohm's Law (V = I * R), the total current can be calculated if the total voltage (V) and total equivalent resistance (Rt) are known:
It = V / Rt
Alternatively, the total current is the sum of the currents through each branch:
It = I1 + I2 + I3 + ...
How to Use the Calculator:
- Enter Resistor Values: Input the resistance in Ohms for each resistor in your parallel circuit. You can enter up to four resistors. If you have fewer than four, leave the unused fields blank.
- Enter Voltage Source (Optional): If you want to calculate the total current, enter the voltage of your power source in Volts. If left blank, only the total resistance will be calculated.
- Click "Calculate": The calculator will display the total equivalent resistance in Ohms and, if a voltage was provided, the total current in Amperes.
Example Calculation:
Consider a parallel circuit with three resistors: R1 = 10 Ohms, R2 = 20 Ohms, and R3 = 30 Ohms, connected to a 12 Volt power source.
1. Calculate Total Equivalent Resistance (Rt):
1 / Rt = 1 / 10 + 1 / 20 + 1 / 30
1 / Rt = 0.1 + 0.05 + 0.03333...
1 / Rt = 0.18333...
Rt = 1 / 0.18333... ≈ 5.45 Ohms
2. Calculate Total Current (It):
It = V / Rt
It = 12 V / 5.45 Ohms ≈ 2.20 Amperes
Using the calculator with these values will yield approximately 5.45 Ohms for total resistance and 2.20 Amperes for total current.