Electrical and Electronic Principles and Technology: Electrical Power

1. Basic Electrical Principles

1.2. Electrical Power

1. What is an Electrical Circuit?

An electrical circuit is a closed loop that allows current to flow through a path consisting of components like resistors, capacitors, power sources, switches, etc.

2. Basic Circuit Components

Component	Symbol	Function
Battery / Cell	🔋	Provides voltage (electrical energy source)
Resistor	▭▭	Limits current, provides resistance
Switch	🔘	Opens/closes the circuit
Wire	—	Connects components (assumed to have no R)
Lamp / Bulb	💡	Emits light when current passes
Capacitor
Ammeter	(A)	Measures current (in series)
Voltmeter	(V)	Measures voltage (in parallel)

3. Electric Current (I)

Flow of electric charge (electrons)
Measured in Amperes (A)

I = \frac{Q}{t}

$I = t Q$

4. Voltage (V) / Potential Difference

Energy per unit charge
Measured in Volts (V)

V = \frac{W}{Q}

$V = Q W$

5. Resistance (R)

Opposition to the flow of current
Measured in Ohms (Ω)

R = \frac{V}{I}

$R = I V$

6. Ohm’s Law

V = IR

$V = I R$

7. Types of Circuits

➤ Series Circuit:

Components connected end-to-end
Same current through all components
Voltage divides across components

Formulas:

R_{\text{eq}} = R_1 + R_2 + \dots

$R eq = R 1 + R 2 + \dots$

V_{\text{total}} = V_1 + V_2 + \dots

$V total = V 1 + V 2 + \dots$

I = \text{same for all}

$I = same for all$

➤ Parallel Circuit:

Components connected across the same two points
Same voltage across each component
Current divides between branches

Formulas:

\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots

$R eq 1 = R 1 1 + R 2 1 + \dots$

V = \text{same for all}

$V = same for all$

I_{\text{total}} = I_1 + I_2 + \dots

$I total = I 1 + I 2 + \dots$

8. Kirchhoff’s Laws

Kirchhoff’s Current Law (KCL):

Total current entering a junction = total current leaving

\sum I_{\text{in}} = \sum I_{\text{out}}

$\sum I in = \sum I out$

Kirchhoff’s Voltage Law (KVL):

Sum of voltage changes around any closed loop = 0

\sum V = 0

$\sum V = 0$

9. Power in Circuits

P = VI = I^2R = \frac{V^2}{R}

$P = V I = I 2 R = R V 2$

10. Measuring Instruments

Instrument	Connected in	Measures
Ammeter	Series	Current (A)
Voltmeter	Parallel	Voltage (V)
Multimeter	Both	V, A, Ω
Galvanometer	Series (low I)	Small currents

11. Capacitors in Circuits

In Series:

\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots

$C eq 1 = C 1 1 + C 2 1 + \dots$

In Parallel:

C_{\text{eq}} = C_1 + C_2 + \dots

$C eq = C 1 + C 2 + \dots$

12. Time-Dependent Circuits (RC Circuits)

Charge/discharge of a capacitor over time

V(t) = V_0 e^{-t/RC}

$V (t) = V 0 e - t / RC$

Q(t) = Q_0 (1 - e^{-t/RC})

$Q (t) = Q 0 (1 - e - t / RC)$

$RC$
RC is the time constant (in seconds)

13. Important Circuit Symbols (in ASCII)

Symbol	Representation
Battery	---
Resistor	—▭— or —//—
Capacitor	—
Switch	—o/ o—
Ground	⏚
Wire Junction	●

14. Common Mistakes to Avoid

Confusing series vs parallel voltage/current rules
Incorrect instrument placement (ammeter in parallel = 🔥!)
Ignoring internal resistance of batteries
Forgetting unit conversions (e.g., mA → A, kΩ → Ω)

Summary Sheet

Quantity	Formula	Units
Current	$I = \frac{Q}{t}$ $I = t Q$	Amperes (A)
Voltage	$V = IR$ $V = I R$	Volts (V)
Resistance	$R = \frac{V}{I}$ $R = I V$	Ohms (Ω)
Power	$P = VI$ $P = V I$	Watts (W)
Energy	$E = Pt$ $E = Pt$	Joules (J)