Series connection of Resistors

The following applies in general for series connection:

The same current flows through each part of a series circuit.
There is only one current

Voltage applied to a series circuit is equal to the sum of the individual voltage drops.

V_t = V₁ + V₂ + … + V_n (1)

The total resistance of a series circuit is equal to the sum of individual resistances.

R_t = R₁ + R₂ + … + R_n (2)

We proof this:

Eq. (1) divided by I:

V_t = V₁ + V₂ + … + V_n
.I I I I

=> According to the Law of Ohm we get equation (2).

Work order: Calculate the necessary series resistor!

Work order - Series Resistor

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First calculate the necessary current for the lamp:

P_L = V_L * I => I = P_L / V_L = 2W / 12V = 0,167 A

Then you can apply the Law of Ohm. Note:

V_RV = V_Bat - V_L = 24 V - 12 V = 12 V

R_V = V_RV = 12 V = 71,86 Ω
. I 0,167 A

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