Direct Current Circuits

Electrolytes are solutions that can transfer charge from electrodes (dissimilar materials).

A potential difference (V) will exist between the electrodes that can be connected to a wire, or light bulb, etc.

Several cells connected are called a battery, although a single cell is also

called a battery

When a continuous conducting path is created between the terminals, an electric circuit is produced.

Electric current (I) is the net charge passing per unit of time:

I = Q∆t

units:ampere A = C/s

In order to produce a circuit, a loop of wire needs to be connected across the potential difference of the cell.The wire (and anything connected to it) will put up a resistance to the flow of electrons.

The current (I) will depend directly on the potential difference (V) and inversely upon the resistance in the circuit (R)

This is Ohm’s Law!

I =V

R

Resistance is measured in units called ohms (Ω)

Resistance is both internal (r) and external.Internal resistance would be the resistance of the wires and cells. It is less than the external resistance(s).Total resistance would be the sum of the internal and external resistances:

RT = r + Rext

Rext would be the sum of all external resistances resolved

Combination of Cells

Cells can be connected in series or parallel:Series: direct connection between anode (+) and cathode (-):

Parallel: direct connection from + to + and - to -

The total electromotive force (emf) of the system depends upon the configuration:

emf = total potential difference (VT)

When connected in series, the emf of the battery equals the sum of the emf of each cell: Three 1.5 V cells connected in series:

VT = V1 + V2 + V3 = 4.5 V

Two 1.5 V cells connected in parallel:

When connected in parallel, the emf of each cellis also the total emf:

VT = V1 = V2 = 1.5 V

Series and Parallel Circuits

Resistances can be connected in series and in parallel as well:

Series: Current does NOT split among R’s:

Req = R1 + R2 + R3

Parallel: Current will split among resistors- more resistance, less current:

I1 = I2 = I3

The current splits up among resistors in parallel according to the resistance.

The potential difference is constant among the resistors ( V = IR)

The equivalent resistance by substitution:

1 = 1 + 1 + 1

Req R1 R2 R3

When simplifying a circuit, always simplify the parallel parts of the circuit first

A 1.5 V dry cell runs an external load of 2.8 . An ammeter in the external part of the circuit reads .50 A. What is the internal resistance of the cell?

VT = 1.5 V

Rext = 2.8 I = .50 A

r = ?

r = RT - Rext

RT = V/I = 1.5 V/.50 A = 3.0

r = 3.0 - 2.8 = .2

r = .50 R1=3.5

R3= 6.0

each cell: 2.0 V

R2 = 3.0

Find A1, A2, A3, V2, V3

R1

R2

R3

R4R5

R6

R7

R8 R9

R10

R11

each cell: 2.0 V

each R = 1.0

Find total current:

R1 R2

R3R4

R6

R5

emf (V)

I (A)

R ()

cell 2.0

R1 5.0

R2 3.5

R3 1.5

R4 4.0

R5 1.0

R6 2.0