Experimenting – Learning – Understanding Key formulae for Electrical Engineering Ohm´s law

A

I U R

U = IR

I R

V

U

Current in A Voltage in V Resistance in Ω

1V 1Ω = 1A

Resistors connected in series

I

1

U

2

U

U = U1 + U2 + U3 + ... R = R1 + R2 + R3 + ...

1

R

2

R

I =

U R

3

3

U U U U = 1 = 2 = 3 R3 R R1 R2

U

U Total voltage in V U1, U2 Voltages across individual resistors in V R Total resistance in Ω R1, R2 Resistance of individual resistors in Ω

Resistors connected in parallel

U

I I

1

R

1

I

2

I I1, I2

1 1 1 1 = + + ... + R R1 R2 R3

R

U

R

2

I

I = I1 + I2 + I3 + ... G = G1 + G2 + G3 + ...

= I •R

=

I1 • R1 = I2 • R2

3

R

3

Total current in A Current through individual resistors in A Total resistance in Ω

G Overall conductance in S G1, G2 Conductance of individual resistors in S R1, R2 Resistance of individual resistors in Ω

Kirchhoff´s ﬁrst law (current law)

I

4

I

3

I

5

I

2

I

1

At any junction in an electrical circuit, the sum of currents ﬂowing towards that point is equal to the sum of currents ﬂowing away from that point. Σ Iin = Σ Iout

Example: I1 = 3 A; I2 = 6 A; I3 = 2 A; I4 = 1,5 A; I5 = ? A Solution: I1 + I5 = I2 + I3 + I4 I5 = I2 + I3 + I4 – I1 I5 = 6 A + 2 A + 1,5 A - 3 A I5 = 9,5 A - 3 A = 6,5 A

Kirchhoff´s second law (voltage law)

U1

U2 U5

I

U3

U4

Umlauf

In any closed current loop the directed sum of the electrical potential differences around the loop must be zero. Directed means that if you trace around the loop in a speciﬁc direction (either direction is just as valid) voltages in the same direction as you are tracing are considered positive and those in the opposite direction count as negative.

Example: U1 = 4,5 V; U2 = 1,5 V; U4 = 1 V; U5 = 3 V; U3 = ? V; Solution: U1 + U2 – U5 – U4 – U3 = 0 U3 = U1 + U2 – U4 – U5 = 4,5 V + 1,5 V – 3 V – 1 V U3 = 2 V

ΣU=0 Wheatstone’s bridge To achieve balance (I12 = 0):

1 R

R

X

R

3

N

2

RX R3 = RN R4

RX Unknown resistance in Ω RN Variable resistance in Ω R3, R4 Known bridge resistors in Ω

R

4

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