Electric Circuits

Principle of charge conservation

states that the total electric charge in a closed system does not change

Kirchoff’’s 1st law

States the sum of the currents entering a junction is always equal to the sum of the currents leaving the same junction.

I.e..

In a series circuit current is the same at all points

in a parallel circuit the current divides at the junctions and each branch has a different value

Kirchhoff’s 2nd law

states the sum all voltages in a series circuit is equal to zero

So Voltage in a series circuit is shared across all components and equals the total V

but Voltage in a parallel circuit is equal across each branch

Deriving R total (series circuit)

Using (K1) and ohms law each resistor has the equation

V1 = IR1, V2=IR2 V3=IR3

Using (K2) Vt= V1+V2+V3

Vt = I(R1+R2+R3)

This then simplifies to

Rt = R1+R2+R3

Deriving R total (parallel circuit)

Using (K2) and ohms law each resistor has the equation

Vt/R1 = I1, Vt/R2 = I2, Vt/R3 = I3

Using (K1) Sum of currents entering a junction is equal to that leaving

It = I1 + I2 + I3

It = V/R1 It = V/R2 + V/R3

It = Vt (1/R1 +1/R2 + 1/R3)

1/Rt = 1/R1 +1/R2 + 1/R3