Electric Current, Resistance, Ohm's Law & Power

M. Rocha

Physics 4B

Electric Current

Electricity in motion

Electric Current

Just like water flows whenever there is a altitude difference, electric charge flows whenever there is a voltage difference

g \Delta h

\Delta V

Electric

Potential Difference

(voltage)

Gravitational Potential Difference

\frac{PE_\mathrm{grav}}{mass}

\frac{PE_\mathrm{electric}}{charge}

Electric Current

Electric current is measured in amperes or amps (A)

An ampere is the flow of
1 coulomb of charge per second

1 coulomb = 6.24 x 10^18 e

= 6.24 billion billion electrons

Electric Charge Flow

Drift Velocity and Current Density

Current:

Drift Velocity:

Current Density:

Current from Current Density

If uniform Current Density:

I = J A

Electrical Resistance

For a given pressure, more water passes through a large pipe than a small one

Similarly, for a given voltage, more electric current passes through a large-diameter wire than a small-diameter one

Less resistance

More resistance

Electrical Resistance

Voltage Source

A simple hydraulic circuit is analogous to an electric circuit

Ohm's Law

\mathrm{Current} = \frac{\mathrm{Voltage}}{\mathrm{Resistance}},

I = \frac{V}{R}

The Current flow is proportional to the Voltage and inversely proportional to the Resistance

1 \ ampere = 1 \ \frac{volt}{ohm}

Units:

A potential difference of 1 volt across a circuit with a resistance of 1 ohm will produce a current of 1 ampere

Ohm (symbol Ω) is the unit of resistance

Checkpoint

A typical light bulb has a resistance of about 100 ohms. What is the current flow across a light bulb when connected to an electric socket providing 120 volts?

I = \frac{V}{R} = \frac{120 \ volts}{100 \ ohms} = 1.2 \ amps

I = \frac{V}{R}

Checkpoint

If the resistance across your body is 1000 times greater than a typical light bulb, how much current would flow trough your body if you touch an electric socket? (current = 1.2 amps for the bulb)

\frac{I_\mathrm{you}}{I_\mathrm{bulb}} = \frac{V R_\mathrm{bulb}}{V R_\mathrm{you}} = \frac{1}{1000}

I = \frac{V}{R}

\Rightarrow I_\mathrm{you} = \frac{1}{1000} I_\mathrm{bulb} = .0012 \ amps

Electric Shock

Ohmic Heating

Flowing electrons strike atoms in a conductor, heating the material. For a given voltage the higher the resistance the higher the heating

Toaster

Oven

Light bulb

Fuses and Circuit Breakers

A fuse is designed to melt (due to ohmic heating) when current is too large

Circuit breaker does same job without needing replacement; flip the switch to reconnect

Conductivity and Resistivity

The conductivity σ of a material tells you how much current density you get for given amount of E-field

Units of σ :

= \frac{1}{\Omega \ m}

The resistivity 𝜌 of a material is the inverse of its conductivity

= \frac{\vec{E}}{\vec{J}}

Units of 𝜌 :

[\rho] = \Omega \ m

Electrical Resistance from Resistivity

Circuit Resistors

Electric Power

\mathrm{Power} = \mathrm{Voltage} \times \mathrm{Current} = V I

Units:

1 \ ampere \times 1 \ volt = 1 \ watt = 1 \frac{Joule}{s}

\mathrm{Power} = \frac{\mathrm{Energy}}{\mathrm{Time}}

P = V I = \mathrm{(\frac{Energy}{Charge}) (\frac{Charge}{Time})} = \mathrm{\frac{Energy}{Time}}

Checkpoint

A kilowatt is 1000 watts, and a kilowatt-hour is the amount of energy consumed in one hour at the rate of 1 kilowatt. If electric energy costs 20 cents per kilowatt-hour, what does it cost to operate a 100 watt light bulb for 10 hours?

100 watts x 10 hours (20 cents/kilowatt-hour)

= 1 kilowatt-hour (20 cents/kilowatt-hour)

= 20 cents