# Calculators

**Ohms Law**

In a D.C. circuit the current is directly proportional to the applied voltage and inversely proportional to the resistance.

Current (A) = I

Voltage (V) = V

Resistance = R

**Kirchoff's Laws**

*1st. Law*

At any electrical junction the current flowing into the junction is equal to the sum of currents flowing out of the junction.

Therefore I1 = I2 + I3 + I4

*2nd Law*

The sum of the voltage drop across any complete path of components connected across the voltage supply equals the voltage provided by the power supply.

Therefore V4 = V1 + V2 +V3

**Component Layout**

*Series*

If two components are connected in series and they each have the same resistance the voltage flowing through component is the same (half of the supply voltage)

Therefore V1 = V2 + V3

and the current flowing through each lamp is the same.

*Parallel*

When two components are connected in parallel the voltage appears across both components

Therefore V1 = V2 = V3

The current flowing across the two components are equal but half of the current from the power supply so I1 + I2 = IT

Therefore I1 = I2 +I3

**Impedance**

In A.C. circuits the current is limited by the impedance (Z). Impedance is measured in ohms, and voltage = current (amperes) X impedance (ohms)

U = I x Z

**Inductive Reactance**

In alternating current circuits which set up significant magnetic fields, there is opposition to the current in addition to that caused by the resistance of the wires. This in additional opposition is called inductive reactance.

**Capacitive Reactants**

In alternating current circuits which set up significant magnetic fields, there is opposition to the current in addition to that caused by the resistance of the wires. This in additional opposition is called inductive reactance.

**Impedance in Series Circuit**

Impedance is the name given to the combined effect of resistance (R) and reactance (XL or XC). It is measured in ohms.

For series circuit, impedance (Z) is given by:

*Where*

X = XL for a resistive inductive circuit

X = XC for a resistive capacitive circuit

*And*

X = XC - XL or XL - XC (the larger minus the smaller for a circuit with resistance, capacitance and inductance)

**Star Connections**

Figure 1 shows three loads connected in the star formation to a three phase four wire supply system. Figure 2 shows the phasor diagram, the red to neutral voltage URN is taken as reference and the phase sequence is red, yellow, blue so that the other line to neutral voltages or phase voltages lie as shown. If URN = UYN = UBN and they are equally spaced the system of voltage is balanced.

Let UL be the voltage between any pair of lines (the line voltage) and UP = URN = UYN = UBN (the phase voltage)

Then UL = √ 3UP

and IL = IP

where IL is the current in any line and IP is the current in any load or phase. The power per phase is P = UPIPcos θ and the total power is the sum of the amount of power in each phase

If the currents are equal and the phase angles are the same as in figure 3 the load on the system is balanced, the current in the neutral is zero and the total power is

P = √ 3UL IL cos θ

*Figure 1*

*Figure 2*

*Figure 3*

**Star Connections**

Figure 1 shows three loads connected in the delta or mesh formation to a three phase supply system. Figure 2 shows the phasor diagram of the line voltages with the red to yellow voltage taken as reference.

The voltage applied to any load is the line voltage UL and the line current is the phasor difference between the currents in the two loads connected to that line. If the load currents are all equal and make equal phase angles with their respective voltages the system is balanced and

IL = √ 3IP

The total power under these conditions is

P = √ 3UL IL cos θ

*Figure 1*

*Figure 2*