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
Electric Current, Resistance & Ohm's Law
By Miguel Rocha
Electric Current, Resistance & Ohm's Law
Physics 4B
