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

Summary of Relationships

Direct vs. Alternating Currents

Direct current (DC) is current that flows in only one direction

Alternating current (AC) is current that flows back and forth with alternating direction

The End

Electric Current

The instrument to measure current is called an Ammeter

Due to charge conservation, same current into and out of light bulb

Capacitors

Capacitors are used to store electric potential energy

They produce a short lived current while discharging