Unit 12 Electric Circuits

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 There are two basic types of circuits.

Series Circuits have circuit elements such as resistors, batteries or capacitors one after another. In a series circuit, current does not have a choice; it can only flow through one path.


Parallel Circuits have circuit elements side by side. In a parallel circuit, current can branch out in as many directions as branches in the circuit.

In our previous experiments, we've discovered that there are some rules that govern electric potential and current in both parallel and series circuits. These are Kirchoff's Laws.

Kirchoff's Current Law:

Because current is the rate of flow of electrical charge, current is conserved in circuits. In a series circuit, current remains the same, no matter where it is measured in the circuit.

It = I1 = I2 = I3

In parallel circuits, current is also conserved. The current flowing into a junction splits in such a way that results in some current going through each branch of the circuit. The sum of the current in all of the branches is equal to the total current going into the junction. Likewise, the current that comes out of a parallel circuit is equal to the sum of the currents in each branch of the circuit.

It = I1 + I2 + I3

Kirchoff's Voltage Law:

Voltage is energy per charge. Energy cannot be created or destroyed. In a series circuit, the net voltage "drop" is equal to the voltage "boost" supplied by the power source.

Vt = V1 + V2 + V3

In parallel circuits, voltage across each branch is the same. If there are no other loads in series, the voltage drop across the parallel circuit is equal to the voltage boost provided by the power source.

Vt = V1 = V2 = V3

Resistance

Although conductors allow the flow of charge through them, there is some interference to the flow of charge. One can visualize the flowing charge colliding with atoms of the conducting material. Inevitably, some energy is lost with each collision, though it it is very small. These collisions cause resistance to the flow of current. We can think about electricity much like we think about flowing water. What factors contribute to resistance?

1) Cross Sectional Area (A): If the cross sectional area is small, it is harder for current to flow resulting in more resistance. A larger cross sectional area makes it easier for current to flow and decreases resistance. This explains why appliances that draw lots of current tend to have thicker wire.

R a 1/A

2) Length (l): The longer the conductor, the more collisions there will be between the flowing charge and the conductor's atoms. This increases the resistance.


R a l

3) Resistivity(r):The resistance to flow of current is determined in part by the nature of the material itself. Silver and copper are the two best conductors and have the two lowest resistivities. Other materials that are not as good of a conductor will have a larger resistivity.

Putting it all together, the resistance of a material can be determined by the equation:

R = rl/A

Resistivity is also dependent on the temperature. In general, the resistivity of a conductor increases with temperature. Some materials like semiconductors will have a decrease in resistivity when the temperature increases. Resistivity at any temperature can be calculated by using the following formula:

r = ro(1 + at)

r = resistivity        ro = resistivity at 0 C        a = temperature coefficient       

 t = temperature (C)

If we think of electricity as a flowing fluid, we can think of voltage as a "pressure" pushing the fluid and the rate of flow of the fluid is the current. This analogy can help us visualize how resistance, current and voltage are related. A greater "pressure" will result in an increased flow of fluid. A larger resistance to the flow, will result in a smaller current.

Ohm's Law

As we observed in lab, the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance,

I = V/R or.

V = IR

V = electric potential (volts)                  I = current (amps)                   R = resistance (W)

Resistance in Circuits

Using Kirchoff's Laws for voltage and current, and Ohm's law, we can determine the resistance in a circuit when the resistors are connected in series and parallel.

Series Circuits:

Kirchoff's laws says that the current remains the same throughout a series circuit while the voltage is "divided up" between the loads so that the sum of the voltages is equal to the applied voltage.


  • Kirchoff's Voltage laws in series circuits :Vt = V1 + V2 + V3
  • Substituting IR for V (Ohm's Law): IRt = IR1 + IR2 + IR3
  • Factor out the I: IRt = I(R1 + R2 + R3)
  • Rt = R1 + R2 + R3

Parallel Circuits:

Kirchoff's laws say the voltage across each resistor in parallel is equal to the total voltage and the total current is equal to the sum of the currents through each branch of the parallel circuit.

  • Kirchoff's Voltage laws in parallel circuitsIt = I1 + I2 + I3
  • Substituting V/R for I (Ohm's Law):V/Rt = V/R1 + V/R2 + V/R3
  • Factor out the V: V/Rt = V(1/R1 + 1/R2 + 1/R3)
  • 1/Rt = 1/R1 + 1/R2 + 1/R3


Energy and Power in Electric Circuits.

Obviously electricity supplies us with energy to power our appliances. While units like volts and amps aren't very helpful for visualizing how electricity and energy are related. If we break down the units for volts to Joules / Coulomb and the units for amps to Coulombs / sec, it becomes clearer for us to see that the product of voltage and amps is the power or the rate at which energy is being supplied to a load in a circuit.

Power = Volts X Amps = (Joules / Coulomb) X (Coulombs / sec) = (Joules / sec) = watts

Since Power is Energy / time energy can be calculated by multiplying power by time.

E = VIt

We can use Ohm's law to develop other equations relating resistance to energy and power.

V = IR so        P = VI = (IR)I                                               P = I2R

I = V/R so       P = VI = V(V/R)                                           P = V2/R

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