EMF
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Table of Contents
#UCLA #Y1Q3 #Physics1B
EMF
Key Definitions
DC Circuit - with one-directional flow of charge
Electromotive Force (EMF) - the extra force in a battery (usually from chemical energy) required to push
- represented as the “battery” symbol in a circuit
Ideal Battery - a battery with an internal resistance of 0
EMF
Defined as the potential:
\(\varepsilon = \int \vec f_s \cdot d\vec l\)
Where
\(\vec f_s = \frac{\vec F_s}{q} \left [\frac N C\right]\)
Such that $\vec F_s$ is the actual force in EMF
Power in a Battery
Power supplied by a battery is defined as
\(P=IV=I\varepsilon\)
EMF in a Battery
The total force acting on a charge in a battery is defined as:
\(\vec F_{net} = q(\vec E + \vec f_s)\)
EMF in a Circuit
Due to the internal resistivity of a battery, $r$:
\(\varepsilon = I(R+r)\)
Thus,
\(I=\frac{\varepsilon}{R+r}\)
Therefore, can be written as:
\(V_{battery}=IR=\varepsilon-Ir\)
Circuits
Open Circuits
If external is taken to infinity in a circuit, we can use EMF to find:
\(I=0\)
Thus
\(V_{battery}=\varepsilon-0=\varepsilon\)
I.e. a circuit with infinite external resistance causes current to go to 0 which is just like an open circuit, so the of the battery is itself
Short Circuit
If resistance goes to 0, current is described as
\(I_{max}=\frac{\varepsilon}{r}\)
Because internal resistance is small, it is equivalent to the EMF, thus
\(V=\varepsilon-\varepsilon=0\)
This is a shorted circuit, so the power is given as