### Energy and power in electric circuits

```Energy and power in electric circuits
Va
+
+
Vb
-
I
Circuit element such as
resistor, battery, …
For qVab>0 : charge q looses potential energy., electric force does work on
the charge
Since current is stationary
Charge is not gaining kinetic energy but energy qVab is transferred into
circuit element, e.g., in the form of heat, light, …
For qVab<0 : charge q gains potential energy, circuit element is a source of
emf such as a battery
If I is the current flowing through the element
dQ  I dt
charge passing through
the element in dt
Potential energy of dQ changes by
VabdQ  Vab I dt
Change of energy per time is the electric power, e.g., consumed by the
circuit element
dQ
Vab

dt
Unit: 1VA=1JA/As=1J/s=1W
P  VI
If circuit element is a resistor we obtain
2
V
P  VI  RI 2 
R
Power delivered to a resistor
If circuit element is a source (of emf)
Rate a which source delivers power
P  VI  E  Ir  I  E I  I 2 r
Power dissipated by internal resistance of source
Rate at which work is done on charge by
nonelectrostatic (e.g., chemical) force
An example:
What is the rate at which the battery converts chemical into electrical energy?
chemical to electrical
Pconversion
 E I  12V  2 A  24W
What is the power dissipated by the internal resistance of the battery?
int ernal r of battery
Pdissipated
 I 2r
 4 A2  2  8W
What is the power dissipated by the external resistor R?
external R
Pdissipated
 I 2 R  4 A2  4  16W
Energy conservation
chemical to electrical
conversion
P
(per time):
P
int ernal r of battery
dissipated
+P
external R
dissipated
EI

I r

I R
24W

8W

16W
2
2
```