**Power **can be defined as the **work done **in a given time. In **mechanical terms**, power is indicated in **Horse power **and in **Electrical terms,** it is indicated in **Watts**. The term Horse Power was introduced to denote the power, since the most common source of power in ancient times is the **Horse**. Let us see the power in a Motor and how Resistivity affects conductance.

The **power** in a **Motor** depends on its** Speed** and **Torque** in the shaft. *Torque is the twisting force by the motor.* Motor speed is measured in terms of** RPM (**Revolution Per Minute) and the Torque is measured in terms of **Pound Feet or lb-ft**.

*Horse power or HP can be calculated using the formula*

**HP = 2**** π S T / 33,000**, were **S** is the motor speed in **RPM** and **T** is the torque in **lb-ft**.

The relationship between the Horse Power, Motor speed and the Torque can be expressed as

**HP α ST** (Alpha means proportional)

But in Electric circuits, power is represented in **Watts**. *Watt is the function of both voltage and current*. Power in electric circuits is expressed as

**P = I V**. Where **I **is the current and **V** is the voltage. In other words **Power** is equal to Current multiplied by the Voltage. In an Open circuit, voltage between the two terminals is **Zero** and hence no power is dissipated.

**Power Calculation**

Power (P) in a load can be easily calculated if the **Voltage** **(E)** and **load Resistance** (R) are available.

*Let us first calculate the current consumption of a 3 Ohms load running in 18 volts.*

**I = E / R = 18 V / 3R = 6 Ampere.**

*If current is calculated, then the power consumption P is*

**P = I E = 6 A x 18 V = 108 Watts.**

*If the voltage increases, power consumption also increases. If the same 3 Ohms load is running in 24 volts, then*

**I = 24 V / 3 R = 8 Ampere and Power P = 8 x 24 = 192 Watts**

**Resistance, Resistivity, and Conductivity**

*Electrical resistance** is the opposition to the flow of current through a conductor*. Its opposite condition is **Electrical conductance** which is the *ease at which the current passes*. Resistance is measured in terms of **Ohms (Ω)** and the **Conductance** in **Siemens (S)**. All materials except the Super conductors (Zero resistance), offer resistance to current flow. *A conductor that has uniform cross section area has a resistance proportional to its Resistivity and length*.

*Resistance is the ratio of voltage to current, while conductance is the inverse to resistance*

**Resistance**

**R = E / I**

**Conductance**

** G = I / E**

**Resistivity**

*It is the measure of the strength of the opposition to current by a material*. Materials showing low resistivity conduct current very fast. The unit of Resistivity is **Ohm meter (Ω.m)** and is represented as** ρ (Rho).**

**Conductivity **

It is the *measure of the ability of a material to conduct current*. Conductivity is represented as **σ (Sigma)**. But the symbol **k (Kappa)** is used in electrical engineering and another symbol **ϒ (Gamma)** is also used occasionally. The unit of conductivity is **Siemens per meter or S.m ^{ -1}**.

**Voltage drop in the load**

As the current passes through the conductor to the load, significant **voltage drop** occurs as the length of the conductor increases. In AC circuits, an additional opposition of current develops by the **electromagnetic field** and the **current **within the conductor. This is the **Impedance **and it depends on the **dimension** of the conductor, **frequency **of current and the **magnetic permeability** of the conductor. In AC circuits, the *voltage drop is the product of current and the Impedance (Z) of the conductor.*

If the load is located far away from the source of current, large **sized conductors** are used to reduce the voltage drop as in the case of **power lines** from the distribution transformer.

Heavily loaded circuits (Motor, Machinery, Heater etc) also require large conductors to reduce the voltage drop.

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