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Electric circuits

1 – Definition 

Association of dipoles connected by electric wires.

2 – 2 types of circuits:

Series circuit: the dipoles are on the same branch.

Series circuit
  • Branch circuit: the dipoles belong to two or more branches which have two nodes in common.
Branch circuit

II – The electric current

1 – Definition 

It only circulates in a closed electrical circuit. It circulates from the + terminal to the – terminal of the generator.

2 – Current intensity

Definition: quantity of electricity transported per unit of time. It is measured using an ammeter.

Current intensity
  • I is in A
  • q is in C
  • t is in s

3 – Electric voltage

Electric voltage

The voltage between point A and point B is equal to the electric potential of point A minus the electric potential of point B. UAB = VA-VB U is in V. The electric voltage is measured using a voltmeter. :

Electric voltage

UAC = UAB + UBC: the voltage across an electric wire is zero.

III – laws 

1 – Mesh laws 

Closed path passing through different points of a circuit. The sum of the tensions encountered is zero.

Mesh laws 

The blue current goes through U5, U2, U3, U4. We see that U5 is in the same direction as the current. We will therefore have + U5 unlike U2 which is in the opposite direction, so we will have -U2. The mesh law of the blue current is therefore: U5 – U2 + U3 + U4 = 0V and the mesh law of the red current is therefore: U1 – U5 – U6 = 0V

2 – Law of nodes 

Connection that connects at least three wires. The sum of the intensities of the currents leaving the same node.

Law of nodes

Law of nodes in A: the 3 intensities meet in A therefore: I1 + I2 + I3 = 0A Law of nodes in B: I5 arrives at B therefore: I5 = I2 + I4 Law of nodes in C: I4 arrives at C therefore: I4 = I1 + I3 + I5

IV – Ohm’s law for a resistance in receiver convection

1 – Definition 

A receiver does not supply electricity (eg diode, lamp, resistor …).

A receiver

R : resistor resistance

resistor resistance

G : conductance of the resistor (S) with G = 1 / RI = G x U or U = R x I

V – Association of linear resistors

1 – Serial association

Dipoles are in series when they are crossed by the same current and share the same connection which is not a connection node.

Serial association 

Réq = R1 + R2 In series, the resistances are added.

2 – Parallel association

Dipoles are in parallel when subjected to the same voltage and are connected terminal to terminal.

Parallel association

Geq = G1 + G2Réq = (R1 x R2) / (R1 + R2). In parallel, the conductances add up. Let’s apply all of this:

– voltage divider :

voltage divider

We know that U = R x IR1 and R2 are in series therefore: U = R1 x I + R2 x IU = (R1 + R2) x IDonc I = U / (R1 + R2) U2 only concerns a dipole, we a therefore: U2 = (R2 / (R1 + R2)) x U

– current divider :

current divider

This time we have R1 and R2 in parallel, so: I1 = (R2 / (R1 + R2)) x II2 = (R1 / (R1 + R2)) x I

VI – Generalized Ohm’s Law

– electric motor generator : U = E – RI

Loi d’ohm

– electric motor receiver : U = E + RI

Loi d’ohm

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