The voltage ( V ) or “ potential difference “ of a DC power source is the drop in energy ( J ) that a coulomb ( C ) of charge will experience by traveling through a resistance ( R ) found within a circuit. The current in question flows along a closed, non-diverging route:
According to Ohm’s Law, the magnitude of the current ( I ) flowing through a series circuit is inversely proportional to the resistance that must be overcome:
( V / R ) = I
If a coulomb of charge loses 1 joule of energy as it crosses a single “ X-ohm “ resistor, a ½ joule energy drop will occur each time a coulomb of charge passes through two “ ½ X-ohm “ resistors within the same current pathway. A similar split in energy drops will occur if three “ ⅓ X-ohm “ resistors are situated within the same circuit. This is why resistors within series circuits are sometimes referred to as “ voltage splitters “; however, the resistors need not be divided in such a proportional fashion. Energy cannot be created or destroyed, and the energy drop across a circuit will occur in as many ( or few ) steps as is needed:
Vt = V1 + V2 + V3
V = IR
ItRt = I1R1 + I2R2 + I3R3
Since the same current travels through each resistor, I1, I2, and I3 equal It; thus, the right-hand side of the equation may be factored for convenience:
ItRt = ( It )( R1+ R2 + R3 )
The total resistance of a DC series circuit ( neglecting energy losses ) yields the following intuitive result:
Rt = R1+ R2 + R3
Q: The following resistors are situated along a closed DC current pathway:
R1 = 1.0 kΩ
R2 = 2.2 kΩ
R3 = 4.7 kΩ
R4 = 10 kΩ
What is the total resistance encountered by each coulomb of charge that travels around the circuit?
A: Rt = R1+ R2 + R3 + R4
Rt = 1.0 kΩ + 2.2 kΩ + 4.7 kΩ + 10 kΩ
Rt = 17.9 kΩ
RENAISSANCE PHYSICS 