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.
Vt = V1 + V2 + … + Vn (1)
The total resistance of a series circuit is equal to the sum of individual resistances.
Rt = R1 + R2 + … + Rn (2)
We proof this:
Eq. (1) divided by I:
Vt = V1 + V2 + … + Vn
.I I I I
=> According to the Law of Ohm we get equation (2).
Work order: Calculate the necessary series resistor!
First calculate the necessary current for the lamp:
PL = VL * I => I = PL / VL = 2W / 12V = 0,167 A
Then you can apply the Law of Ohm. Note:
VRV = VBat - VL = 24 V - 12 V = 12 V
RV = VRV = 12 V = 71,86 Ω
. I 0,167 A