Current

Current is the flow of electric charge in a conductor. It is measured in amperes (A) and can be classified into direct current (DC) and alternating current (AC). The behavior of current in three-phase systems is also crucial for industrial applications.

Current in DC Circuits

In DC circuits, current flows in one direction. The relationship between voltage (V), current (I), and resistance (R) is given by Ohm's Law:

Formula: I = V / R

Formula Breakdown:

• I: Current (amperes, A)
• V: Voltage (volts, V)
• R: Resistance (ohms, Ω)

Example Calculation:

• Task: Calculate the current in a DC circuit with a voltage of 12 V and a resistance of 6 Ω.
• Solution: Use the formula I = V / R.
• I = 12 V / 6 Ω = 2 A

Current in AC Circuits

In AC circuits, current alternates in direction and varies in magnitude with time. The relationship between voltage (V), current (I), and impedance (Z) is given by Ohm's Law for AC circuits:

Formula: I = V / Z

Formula Breakdown:

• I: Current (amperes, A)
• V: Voltage (volts, V)
• Z: Impedance (ohms, Ω)

Impedance (Z) combines resistance (R) and reactance (X) and is given by:

Formula: Z = √(R² + X²)

Formula Breakdown:

• Z: Impedance (ohms, Ω)
• R: Resistance (ohms, Ω)
• X: Reactance (ohms, Ω)

Example Calculation:

• Task: Calculate the current in an AC circuit with a voltage of 120 V and an impedance of 10 Ω.
• Solution: Use the formula I = V / Z.
• I = 120 V / 10 Ω = 12 A

Impedance Calculation Form

Current in Three-Phase Systems

In three-phase systems, current can be calculated for both balanced and unbalanced loads. For balanced loads, the line current (I_L) and phase current (I_ph) are related by:

Formula for Star (Wye) Connection: I_L = I_ph

Formula for Delta Connection: I_L = √3 × I_ph

Formula Breakdown:

• I_L: Line current (amperes, A)
• I_ph: Phase current (amperes, A)

Example Calculation for Star Connection:

• Task: Calculate the line current for a star-connected system with a phase current of 10 A.
• Solution: Use the formula I_L = I_ph.
• I_L = 10 A

Example Calculation for Delta Connection:

• Task: Calculate the line current for a delta-connected system with a phase current of 10 A.
• Solution: Use the formula I_L = √3 × I_ph.
• I_L = √3 × 10 A ≈ 17.32 A

Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law states that the total current entering a junction in an electrical circuit must equal the total current leaving the junction. This law is based on the principle of conservation of charge.

Formula: ΣI_in = ΣI_out

Formula Breakdown:

• ΣI_in: Sum of currents entering the junction
• ΣI_out: Sum of currents leaving the junction

Example Calculation:

• Task: Determine the unknown current I_x at a junction where I₁ = 3 A, I₂ = 2 A, and I₃ = 4 A are entering, and I₄ = 7 A is leaving.
• Solution: Apply KCL: ΣI_in = ΣI_out
• • 3 A + 2 A + 4 A = I₄ + I_x
  • 9 A = 7 A + I_x
  • I_x = 2 A

Related: Kirchhoff's Voltage Law