Circuits
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Table of Contents
- Circuits
#UCLA #Y1Q3 #Physics1B
Circuits
Key Definitions
Steady-state circuit - circuit which maintains constant current
Power - the rate of energy delivered or extracted from a circuit
Steady-State Circuits
- Conductors must form a closed loop to maintain a steady
- Additionally, a source of constant voltage must be in the circuit (unless using a superconductor)
- Steady current requires the to be constant and thus the to be constant
Potential in a Circuit
The net change in potential energy for a travelling around a circuit must be zero Thus, the electric potential around a circuit must also be 0. I.e.
\(V_{source}=IR\)
Energy and Power
The power flowing through a circuit is given by:
\(P=IV\)
The power is independent of Ohm’s Law, but if the law is true, then:
\(P=IV=I^2R=\frac{V^2}{R}\)
Circuit Organization
In Series
Potential Difference
\(\Delta V_{eq}=\sum \Delta V_{R_i}\)
Current
\(I_{eq} = I_{R_i}\)
Resistance
\(R_{eq}=\sum R_i\)
Capacitance
\(\frac{1}{C_{eq}}=\sum \frac{1}{C_i}\)
In Parallel
Potential Difference
\(\Delta V_{eq}=\Delta V_{R_i}\)
Current
\(I_{eq}=\sum I_{R_i}\)
Resistance
\(\frac{1}{R_{eq}} = \sum \frac{1}{R_i}\)
Capacitance
\(C_{eq}=\sum C_i\)
Kirchhoff’s Rules
Current/Junction Rule
The current entering a junction is equivalent to the current leaving the junction:
\(\sum I_{in} = \sum I_{out}\)
Voltage/Loop Rule
Because in a DC circuit the draining the current in the circuit is conservative:
\(\oint \vec E \cdot d\vec l = 0\)
Thus in closed loop circuits: