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Calculate The Current I2 in The Following Configuration

Reviewed by Calculator Editorial Team

This calculator helps you determine the current i2 in a given electrical configuration using Ohm's Law and Kirchhoff's Current Law. The calculation is based on the total resistance and voltage in the circuit.

Introduction

Calculating the current i2 in an electrical circuit requires understanding the relationships between voltage, resistance, and current. This guide explains how to determine i2 in a configuration where multiple resistors are connected in series and parallel.

The calculation involves:

  • Identifying the total resistance in the circuit
  • Applying Kirchhoff's Current Law to determine branch currents
  • Using Ohm's Law to find individual currents

Formula

To calculate the current i2 in a given configuration, we use the following steps:

  1. Calculate the equivalent resistance of the circuit
  2. Determine the total current using Ohm's Law (V = IR)
  3. Apply Kirchhoff's Current Law to find branch currents

Equivalent Resistance (Req)

For resistors in series: Req = R1 + R2 + R3 + ...

For resistors in parallel: 1/Req = 1/R1 + 1/R2 + 1/R3 + ...

Total Current (Itotal)

Itotal = V / Req

Branch Current (i2)

i2 = Itotal × (Rparallel / (Rparallel + Rseries))

Worked Example

Consider a circuit with:

  • R1 = 10Ω (series)
  • R2 = 20Ω (parallel with R3)
  • R3 = 30Ω (parallel with R2)
  • V = 12V

Step 1: Calculate equivalent resistance of R2 and R3 in parallel:

1/Req = 1/20 + 1/30 = 0.05 + 0.0333 = 0.0833

Req = 1/0.0833 ≈ 12Ω

Step 2: Calculate total equivalent resistance of the circuit:

Rtotal = R1 + Req = 10 + 12 = 22Ω

Step 3: Calculate total current:

Itotal = 12 / 22 ≈ 0.545A

Step 4: Calculate current through R2 (i2):

i2 = Itotal × (R3 / (R2 + R3)) = 0.545 × (30 / (20 + 30)) ≈ 0.327A

Interpreting Results

The calculated current i2 represents the flow of electrons through resistor R2 in the circuit. This value is crucial for:

  • Power calculations (P = I²R)
  • Voltage drop analysis
  • Component selection

Note: Always verify your circuit configuration matches the calculation assumptions. Different resistor arrangements will yield different current values.

FAQ

What is the difference between series and parallel resistance?

In series, resistors add up directly. In parallel, their reciprocals add up. This affects how current divides through the circuit.

Can I use this calculator for AC circuits?

This calculator is designed for DC circuits. AC circuits require additional considerations like reactance and phase angle.

What if my circuit has more than three resistors?

The calculator can handle any number of resistors by applying the same principles of series and parallel combinations.