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Electric Circuits

Electric circuits transfer energy. Electrical energy is converted into light, heat, sound, mechanical work, etc. The byproduct of any circuit is always heat.

DC current (direct current)
a steady flow of current in one direction

AC current (alternating current)
direction of current flow changes many times a second. In the US, the frequency of change is 60 Hz. Therefore, the current changes direction 120 times per second.

emf (electromotive force)
source of energy moving electrons through the circuit

electric current (symbol is I; SI unit is the ampere, or A)
flow of charge, or current = charge/sec
1 A = 1 C/ sec

conventional current
flow of positive charge

electric power (symbol is P; SI unit is watt)
the rate of doing electrical work
P = VI = (IR)I
P = I2R

SI unit of power; 1 Watt = 1 Joule/sec = 1 VoltAmp

electrical work (symbol is W; SI unit is Joule)
W = P t
W = V I t

resistance (symbol is R,; SI unit is ohm or W)
opposition to current flow
1 W = 1 V/ 1 A

Animation representing a simple circuit

Ohmís law
for a given resistance, the potential difference is proportional to the current flow
V = I R

Resistance of a solid conductor depends upon:
  1. nature of the material
  2. length of the conductor
  3. cross-sectional area of the conductor
  4. temperature

measures small currents

measures current

ammeters and galvanometers are connected in a circuit, positive to positive and negative to negative; they have very low resistance so that the current flow through them is a maximum; they are connected in series

measures potential difference between two points in a circuit

voltmeters are connected in a circuit, positive to negative and negative to positive. They have very high resistance so that the current flow through them is a minimum; they are connected in parallel

Circuit symbols

circuit symbols

Series Circuits

Series circuit
resistors are connected so that there is only one path for the current to flow through the resistors; the current is the same at all points - current is constant in series

effective resistance (equivalent resistance)
the resistance of a single resistor that could replace all the resistors in a series circuit

Kirchoffís second law
in any closed circuit loop, the potential energy drops of the individual electrical devices equals the total energy of the circuit; this is a statement of the law of conservation of energy

As resistors are added in series, total resistance increases and total current decreases.

Steps in simplifying series circuits:

  1. find the effective resistance of the circuit
  2. find the total current using Ohmís law
  3. apply Ohmís law to each individual resistor to determine the individual resistorís voltage drop

Series Circuit Animation

Parallel Circuits

Parallel circuits
resistors in parallel have the same voltage drop across them. The sum of the currents in each parallel branch equals the total current entering the parallel branch of resistors. Voltage is constant in parallel.

Kirchoffís first law
the sum of the currents entering a point is equal to that of the currents leaving the point.

In a parallel circuit, all the resistors in parallel can be replaced with one equivalent resistance that carries the same current and has the same voltage drop across it.

As resistors are added in parallel, total resistance decreases and total current increases.

Power companies maintain a house voltage of 120 V. House appliances are connected in parallel. The more appliances on a circuit, the lower the total resistance, the greater the current. Fuses protect against circuit overloading.

Steps in simplifying parallel circuits:

  1. find the equivalent resistance
  2. use Ohmís law to find total current
  3. apply Ohmís law to each resistor to find the current in that branch

Parallel Circuit Animation

Complex Circuits

Complex circuits are a combination of resistors in parallel and in series.

Steps in simplifying complex circuits:

  1. determine the equivalent resistance of each set of resistors in parallel
  2. determine the total resistance of the circuit
  3. determine total current
  4. calculate voltage drops across all series resistors
  5. calculate currents in each parallel branch

Electric Circuits Sample Problems

Electric Circuits Homework