Direct Current & Circuits
Electric Current
The rate of flow of charge through a cross-sectional area is called the electric current. If the rate is constant, the current I is given by
(1)
where 
is
the magnitude of the charge crossing a surface in a time 
,
the surface being perpendicular to the motion of the charge. The SI
unit for current is the coulomb per second 
,
which is referred to as an ampere (A).
(a) The direction of an electric current is the direction of flow of positive charge. (b) Thus, it is opposite to the flow of negative charge.
Example 17-1
The disk drive in a portable CD player is connected to a battery that supplies it with a current of 0.22 A. How many electrons pass through the drive in 4.5 s?
The Battery
The voltaic pile, in which the elementary cell was a zinc-card-board-silver sandwich.
A single voltaic wet cell and three wired in series to form a battery.
Electromotive Force:
the emf, 
,
is the voltage measured across the terminals of a source when no current
is being drawn from or delivered to it.
Batteries are made of cells. You can put the cells in either series or parallel. Series – the voltage across a series connected battery is the sum of the voltages across each constituent cell.
Cells connected in series the voltages add up and point D is 4.5 V above point A.
Cells connected as above the voltages subtract and the A and C are at the same potential.
Parallel – voltage across the battery is the voltage across each cell. The current through the load is the sum of the currents provided by each cell.
Example 17-2
A battery with an emf of 1.5 V delivers a current of 0.44 A to a flashlight bulb for 64 s. Find (a) the charge that passes through the circuit and (b) the work done by the battery.
Example 17-3
A small cell has an emf of 0.80 V and can supply 10.0 mA under normal operating conditions. How should a battery be constructed if it is to have an emf of 12.0 V and an operating current of 30.0 mA? How many cells will be needed?
Resistance
When electrons move through a wire they encounter resistance to their motion. In order to move electrons against this resistance, it is necessary to apply a potential difference between the ends of the wire.
Ohm's Law
V = IR
Example 17-4
A potential difference
of 24 V is applied to a 150 
resistor.
How much current flows through the resistor?
Resistivity
Definition of Resistivity, 
where ,
is the resistivity for each substance (Table 17-2, p. 618), L is the
length of the wire, and A is the cross-sectional area of the wire.
The resistivity of a substance is also dependent on the temperature of the substance. The higher the temperature of the substance the greater the resistance.
where 
,
is the Temperature Coefficients of Resistivity (Table 17-3, p. 619).
Example 17-5
Wire 1 has a length and a circular cross section of diameter D. Wire 2 is constructed from the same material as wire 1 and has the same shape, but its length is 2L, and its diameter is 2D. Is the resistance of wire 2 (a) the same as that of wire 1, (b) twice that of wire 1, or (c) half that of wire 1?
Example 17-6
A current of 1.82 A flows through a copper wire 1.75 m long and 1.10 mm in diameter. Find the potential difference between the ends of the wire.
Superconductivity
Below a certain critical temperature, 
,
certain materials lose all electrical resistance and current flowing
in a superconductor can continue undiminished as long as its temperature
is maintained below .
Resistance versus Temperature of a thallium compound (blue) and a europium compound (red).
Energy and Power
In general, energy is required to cause an electric current to flow through a circuit. The rate at which the energy must be supplied is the power.
Electrical Power
or
or
Units 
Example 17-7
A handheld electric fan operates on a 3.00 V battery. If the power generated by the fan is 2.24 W, what is the current supplied by the battery?
Example 17-8
A battery that produces a potential difference V is connected to a 5 W light bulb. Later, the 5 W light bulb is replaced with a 10 W light bulb. (a) In which case does the battery supply the greatest current? (b) Which light bulb has the greatest resistance?
Example 17-9
A battery with an
emf of 12 V is connected to a 545 resistor.
How much energy is dissipated in the resistor is 65 s?
Energy Usage
Example 17-10
A holiday goose is cooked in the kitchen oven for 4.00 h. Assume that the stove draws a current of 20.0 A, operates at a voltage of 220.0 V, and uses electrical energy that costs $0.048 per kWh. How much does it cost to cook your goose?
