Answer:
Choice A. P = I² · R where
- P is the power in the DC circuit,
- I is the current through the circuit, and
- R is the total resistance of the circuit.
Step-by-step explanation:
Electrical power is the rate at which the electrical force does work. So what is electrical work? That's the work [tex]W[/tex] that the electrical force do when it moves charges [tex]Q[/tex] across a potential difference [tex]V[/tex]:
W = [tex]V\cdot Q[/tex].
The power is the rate at which the electrical force do the work:
[tex]\displaystyle P = \frac{W}{t} = V \cdot \frac{Q}{t}[/tex].
On the other hand, current [tex]I[/tex] is the charge through a cross-section of the circuit in unit time. By the definition of current:
[tex]\displaystyle\frac{Q}{t} = I[/tex].
[tex]\displaystyle P =V \cdot \frac{Q}{t} = V\cdot I[/tex].
Consider Ohm's Law:
[tex]V = I \cdot R[/tex].
Therefore
[tex]\displaystyle P = V\cdot I = (I \cdot R) \cdot I = I^{2}\cdot R[/tex].
