## Ohm’s Law

3-1: The Current *I *= *V/R*

3-2: The Voltage *V* = *IR*

3-3: The Resistance* R* = *V/I*

3-4: Practical Units

3-5: Multiple and Submultiple Units

3-6: The Linear Proportion between *V* and *I*

3-7: Electric Power

3-8: Power Dissipation in Resistance

3-9: Power Formulas

3-10: Choosing a Resistor for a Circuit

3-11: Electric Shock

3-12: Open-Circuit and Short-Circuit Troubles

## Ohm’s Law Formulas

- There are three forms of Ohm’s Law:
*I = V/R *
*V = IR *
*R = V/I*

where:

*I *= Current
*V* = Voltage
*R* = Resistance

## The Current *I *= *V/R*

*I = V/R*
- In practical units, this law may be stated as:
- amperes = volts / ohms

## Practical Units

The three forms of Ohm’s law can be used to define the practical units of current, voltage, and resistance:

- 1 ampere = 1 volt / 1 ohm
- 1 volt = 1 ampere × 1 ohm
- 1 ohm = 1 volt / 1 ampere

## Multiple and Submultiple Units

**Units of Voltage**

- The basic unit of voltage is the
**volt (V).**
- Multiple units of voltage are:
**kilovolt (kV)**

1 thousand volts or 103 V
**megavolt (MV)**

1 million volts or 106 V
- Submultiple units of voltage are:
**millivolt (mV)**

1-thousandth of a volt or 10-3 V
**microvolt (****μ****V)**

1-millionth of a volt or 10-6 V

**Units of Current**

- The basic unit of current is the
**ampere (A).**
- Submultiple units of current are:
**milliampere (mA)**

1-thousandth of an ampere or 10-3 A
**microampere (****μ****A)**

1-millionth of an ampere or 10-6 A

**Units of Resistance**

- The basic unit of resistance is the
**Ohm (****Ω****).**
- Multiple units of resistance are:
**kilohm (kW)**

1 thousand ohms or 103 Ω
**Megohm (MW)**

1 million ohms or 106 Ω

**The Linear Proportion between ***V* and *I*

- The Ohm’s Law formula
*I = V/R* states that *V* and* I *are directly proportional to any one value of *R.*
- Fig. 3.5: Experiment to show that
*I* increase in direct proportion to *V* with the same *R*. (*a*) Circuit with variable *V* but constant *R*. (*b*) Table of increasing *I* for higher *V.* (*c*) Graph of *V* and *I* values. This is a linear volt-ampere characteristic. It shows a direct proportion between *V* and *I.*

**When V is constant:**

*I* decrease as *R* increases.
*I *increase as *R* decreases.

**Examples:**

- If
*R* doubles,* I* is reduced by half.
- If
*R* is reduced to ¼, *I* increase by 4.
- This is known as an
*inverse relationship*.

**Linear Resistance**

- A linear resistance has a constant value of ohms. Its
*R* does not change the applied voltage, so *V* and *I *are directly proportional.
- Carbon-film and metal-film resistors are examples of linear resistors.

**Nonlinear Resistance**

- In a nonlinear resistance, increasing the applied
*V* produces more current, but *I *do not increase in the same proportion as the increase in *V*.
- Example of a Nonlinear Volt–Ampere Relationship:
- As the tungsten filament in a light bulb gets hot, its resistance increases.

- Another nonlinear resistance is a
**thermistor. **
- A thermistor is a resistor whose resistance value changes with its operating temperature.
- As an
**NTC** **(negative temperature coefficient)** thermistor gets hot, its resistance decreases.

**Electric Power**

**The basic unit of power is the watt (W).**

- Multiple units of power are:
**kilowatt (kW):**

1000 watts or 103 W
**megawatt (MW):**

1 million watts or 106 W
- Submultiple units of power are:
**milliwatt (mW):**

1-thousandth of a watt or 10-3 W
**microwatt (****μ****W):**

1-millionth of a watt or 10-6 W

- Work and energy are basically the same, with identical units.
- Power is different. It is the
__time rate__ of doing work.
- Power = work / time.
- Work = power × time.

**Practical Units of Power and Work:**

- The rate at which work is done (power) equals the product of voltage and current. This is derived as follows:
- First, recall that:
- 1 volt = 1 joule / 1 coulomb
- 1 ampere = 1 coulomb / 1 second

Power = Volts × Amps, or *P = V **×** I*

**Kilowatt Hours**

- The kilowatt-hour (kWh) is a unit commonly used for large amounts of electrical work or energy.
- For example, electric bills are calculated in kilowatt hours. The kilowatt-hour is the billing unit.
- The amount of work (energy) can be found by multiplying power (in kilowatts) × time in hours.

**To calculate the electric cost, start with the power:**

- An air conditioner operates at 240 volts and 20 amperes.
- The power is
*P = V *×* I* = 240 × 20 = 4800 watts.
__Convert to kilowatts__:

4800 watts = 4.8 kilowatts

__Multiply by hours__: (Assume it runs half the day)

energy = 4.8 kW × 12 hours = 57.6 kWh

__Multiply by rate__: (Assume a rate of $0.08/ kWh)

cost = 57.6 × $0.08 = $4.61 per day

**Power Dissipation in Resistance**

- When current flows in a resistance, heat is produced from the friction between the moving free electrons and the atoms obstructing their path.
- Heat is evidence that power is used in producing current.

- The amount of power dissipated in a resistance may be calculated using any one of three formulas, depending on which factors are known:
*P = I**2**×**R*
*P = V**2 **/ R*
*P = V**×**I*

**Power Formulas**

- Combining Ohm’s Law and the Power Formula
- All nine power formulas are based on Ohm’s Law.
- Substitute
*IR* for *V* to obtain:
*P = VI*
* = (IR)I *
* = I**2**R*

**Combining Ohm’s Law and the Power Formula**

- Substitute
*V/R* for *I* to obtain:
*P = VI*
* = **V **×** V/ R*
* = V**2** / R*

**Choosing a Resistor for a Circuit**

- Follow these steps when choosing a resistor for a circuit:
- Determine the required resistance value as
*R = V / I.*
- Calculate the power dissipated by the resistor using any of the power formulas.
- Select a wattage rating for the resistor that will provide an adequate cushion between the actual power dissipation and the resistor’s power rating.

**Maximum Working Voltage Rating**

- A resistor’s maximum working voltage rating is the maximum voltage a resistor can withstand without internal arcing.
- The higher the wattage rating of the resistor, the higher the maximum working voltage rating.

**Maximum Working Voltage Rating**

- With very large resistance values, the maximum working voltage rating may be exceeded before the power rating is exceeded.
- For any resistor, the maximum voltage which produces the rated power dissipation is:
*V*max =

- Maximum Working Voltage Rating
- With very large resistance values, the maximum working voltage rating may be exceeded before the power rating is exceeded.
- For any resistor, the maximum voltage which produces the rated power dissipation is:
*V*max = *P *rating × *R*

**Electric Shock**

- When possible, work only on circuits that have the power shut off.
- If the power must be on, use only one hand when making voltage measurements.
- Keep yourself insulated from earth ground.
- Hand-to-hand shocks can be very dangerous because current is likely to flow through the heart!

**Open-Circuit**

An open circuit has zero current flow.

**Short-Circuit**

- A short circuit has excessive current flow.
- As
*R* approaches 0, *I* approach ¥.

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