electric circuits
Physics Notes: Electric Circuits
Electrical Quantities
Quantity | Definition | Unit | Formula |
|---|---|---|---|
Voltage (Potential Difference) | Energy difference per unit charge between two points | Volt (V) | (V = IR) |
Current | Flow of electric charge | Ampere (A) | (I = \frac{V}{R}) |
Resistance | Opposition to current flow | Ohm (Ω) | (R = \frac{V}{I}) |
Power | Rate at which electrical energy is converted | Watt (W) | (P = IV) |
Ohm's Law
[
V = IR
]
Rearranged:
[
I=\frac{V}{R}
]
[
R=\frac{V}{I}
]
Series Circuits
Characteristics
Only one path for current.
Current is the same everywhere.
Voltage is shared among components.
Adding resistors increases total resistance.
If one component fails, the whole circuit stops working.
Rules
Current
[
I_{\text{total}}=I_1=I_2=I_3
]
Current stays constant.
Voltage
Total voltage equals the sum of voltage drops.
[
V_{\text{source}}=V_1+V_2+V_3+\cdots
]
Equivalent Resistance
[
R_{\text{eq}}=R_1+R_2+R_3+\cdots
]
Equivalent resistance is greater than any individual resistor.
Current Formula
[
I=\frac{V_{\text{source}}}{R_{\text{eq}}}
]
Example
Given:
(R_1=24\Omega)
(R_2=38\Omega)
(V=120V)
Step 1
Equivalent resistance:
[
R=24+38=62\Omega
]
Step 2
Current:
[
I=\frac{120}{62}=1.9A
]
Answer
Equivalent resistance = 62 Ω
Current = 1.9 A
Parallel Circuits
Characteristics
Multiple current paths.
Voltage is the same across every branch.
Current splits between branches.
Adding resistors decreases equivalent resistance.
One failed branch usually does not stop the others.
Voltage
[
V_{\text{total}}=V_1=V_2=V_3
]
Current
[
I_{\text{total}}=I_1+I_2+I_3+\cdots
]
Current Through Each Branch
[
I=\frac{V}{R}
]
Lower resistance → Higher current.
Higher resistance → Lower current.
Equivalent Resistance
[
\frac{1}{R_{\text{eq}}}
\frac{1}{R_1}
+
\frac{1}{R_2}
+
\frac{1}{R_3}
+\cdots
]
Equivalent resistance is always smaller than the smallest resistor.
Combined Circuits
A combined circuit contains both series and parallel sections.
Steps to Solve
Draw the circuit (if not provided).
Simplify all parallel sections into one equivalent resistor.
Simplify any series sections.
Repeat until only one resistor remains.
Find total current using:
[
I=\frac{V}{R_{\text{eq}}}
]
Work backward to find currents and voltages in each branch if needed.
Power
Power measures how quickly electrical energy is used.
Formula:
[
P=IV
]
Units:
Watt (W)
Digital Multimeter
Measures:
Voltage (V)
Current (A)
Resistance (Ω)
Key Differences
Series | Parallel |
|---|---|
One current path | Multiple current paths |
Current is the same | Voltage is the same |
Voltage is divided | Current is divided |
Resistances add | Reciprocals add |
Adding resistors increases resistance | Adding resistors decreases resistance |
One broken component stops entire circuit | Other branches continue working if one fails |
Essential Formulas
Ohm's Law
[
V=IR
]
[
I=\frac{V}{R}
]
[
R=\frac{V}{I}
]
Power
[
P=IV
]
Series
[
R=R_1+R_2+R_3
]
[
V=V_1+V_2+V_3
]
[
I=\text{constant}
]
Parallel
[
\frac{1}{R}
\frac{1}{R_1}
+
\frac{1}{R_2}
+
\frac{1}{R_3}
]
[
V=\text{constant}
]
[
I=I_1+I_2+I_3
]
Quick Memory Tricks
Series = Same Current, Sum Voltage, Sum Resistance
Parallel = Same Voltage, Sum Current, Reciprocal Resistance
Series: Resistance ↑ → Current ↓
Parallel: More branches → Resistance ↓ → Total Current ↑