1st Year Trade Theory Formulas

⚡ ITI Electrician 1st Year – Complete Formula Sheet (With Units)

Comprehensive list of formulas for ITI Electrician 1st Year Trade Theory.

⚡️Electric Charge

\[Q = I \times t\]

Quantity	Symbol	Unit
Charge	Q	Coulomb (C)
Current	I	Ampere (A)
Time	t	Second (s)

🧮 Ohm’s Law

\[V = I \times R\]

Quantity	Symbol	Unit
Voltage	V	Volt (V)
Current	I	Ampere (A)
Resistance	R	Ohm (\(\Omega\))

🧮 Resistance – Derived Formulas

\[R = \frac{V}{I}\] \[R = \frac{W}{I^2}\] \[R = \frac{V^2}{W}\]

Formula	Based On	Unit
\(R = \frac{V}{I}\)	Ohm’s Law	Ohm (\(\Omega\))
\(R = \frac{W}{I^2}\)	Power Formula \(W = I^2 R\)	Ohm (\(\Omega\))
\(R = \frac{V^2}{W}\)	Power Formula \(W = \frac{V^2}{R}\)	Ohm (\(\Omega\))

🔗 Resistors in Series & Parallel

Resistors in Series:

\[R_{\text{total}} = R_1 + R_2 + \ldots + R_n\]

Resistors in Parallel:

\[\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots + \frac{1}{R_n}\]

Quantity	Symbol	Unit
Resistance	R	Ohm (\(\Omega\))
Total Resistance	\(R_{total}\)	Ohm (\(\Omega\))

🧲 Inductors in Series & Parallel

Inductors in Series:

\[L_{\text{total}} = L_1 + L_2 + \cdots + L_n\]

Inductors in Parallel:

\[\frac{1}{L_{\text{total}}} = \frac{1}{L_1} + \frac{1}{L_2} + \cdots + \frac{1}{L_n}\]

Quantity	Symbol	Unit
Inductance	L	Henry (H)
Total Inductance	\(L_{total}\)	Henry (H)

📏 Resistivity & Conductivity

Resistivity Formula:

\[R = \rho \frac{L}{A}\]

Conductivity Formula:

\[\sigma = \frac{1}{\rho}\]

Quantity	Symbol	Unit
Resistance	R	Ohm (\(\Omega\))
Resistivity	\(\rho\)	Ohm-meter (\(\Omega \cdot m\))
Length	L	Meter (m)
Area (Cross-section)	A	Meter² (m²)
Conductivity	\(\sigma\)	Siemens/meter (S/m)

🔁 Kirchhoff’s Laws

KCL (Kirchhoff’s Current Law):

The algebraic sum of currents entering a junction is equal to the algebraic sum of currents leaving the junction.

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

Unit for Current: Ampere (A)

KVL (Kirchhoff’s Voltage Law):

The algebraic sum of all voltages around any closed loop in a circuit is equal to zero.

\[\sum V = 0\]

Unit for Voltage: Volt (V)

🧲 Electromagnetic Induction (Faraday's Law)

\[e = -N \frac{d\phi}{dt}\]

Quantity	Symbol	Unit
Induced EMF	e	Volt (V)
Number of Turns	N	Unitless
Magnetic Flux	\(\phi\)	Weber (Wb)
Time	t	Second (s)
The negative sign indicates the direction of the induced EMF (Lenz's Law).

🔌 Capacitors in Series & Parallel

Capacitors in Series:

\[\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}\]

Capacitors in Parallel:

\[C_{\text{total}} = C_1 + C_2 + \cdots + C_n\]

Quantity	Symbol	Unit
Capacitance	C	Farad (F)
Total Capacitance	\(C_{total}\)	Farad (F)

🧮 Electrical Energy

\[E = P \times t\]

Quantity	Symbol	Unit
Energy	E	Watt-hour (Wh), Kilowatt-hour (kWh), Joule (J)
Power	P	Watt (W)
Time	t	Hour (h) or Second (s)

💡 Electric Work

\[W = V \times I \times t\]

Quantity	Symbol	Unit
Work Done	W	Joule (J)
Voltage	V	Volt (V)
Current	I	Ampere (A)
Time	t	Second (s)

🔥 Joule’s Law of Heating

\[H = I^2 R t\]

Quantity	Symbol	Unit
Heat Produced	H	Joule (J)
Current	I	Ampere (A)
Resistance	R	Ohm (\(\Omega\))
Time	t	Second (s)

🔋 Electric Power (DC) – 3 Formulas

\[P = V \times I\] \[P = I^2 \times R\] \[P = \frac{V^2}{R}\]

Quantity	Symbol	Unit
Power	P	Watt (W)
Voltage	V	Volt (V)
Current	I	Ampere (A)
Resistance	R	Ohm (\(\Omega\))

⚡AC Power – Single & Three Phase

\[P = V \times I \times \cos\phi \quad
\] \[\text{(Single Phase)}\] \[P = \sqrt{3} \times V \times I \times \cos\phi \quad \]\[\text{(Three Phase)}\]

Quantity	Symbol	Unit
Active Power	P	Watt (W)
Line Voltage	V	Volt (V)
Line Current	I	Ampere (A)
Power Factor	\(\cos\phi\)	Unitless

⚡ Types of Power

\[ \text{Single Phase}\] \[S = V \times I \] \[P = V \times I \times \cos\phi \] \[Q = V \times I \times \sin\phi \] \[\] \[ \text{Three Phase}\] \[S = \sqrt{3} \times V \times I \] \[P = \sqrt{3} \times V \times I \times \cos\phi \] \[Q = \sqrt{3} \times V \times I \times \sin\phi \] \[\] \[ \text{Power Triangle}\] \[S^2 = P^2 + Q^2 \]

Quantity	Symbol	Unit
Apparent Power	S	Volt-Ampere (VA)
Active Power	P	Watt (W)
Reactive Power	Q	Volt-Ampere Reactive (VAR)
Power Factor Angle	\(\phi\)	Radian / Degree

🧠 Power Factor – 3 Formulas

\[\cos\phi = \frac{P}{S}\] \[\cos\phi = \frac{R}{Z}\] \[\cos\phi = \frac{1}{\sqrt{1 + \left( \frac{Q}{P} \right)^2 }}\]

Quantity	Symbol	Unit
Power Factor	\(\cos\phi\)	Unitless
Active Power	P	Watt (W)
Apparent Power	S	VA
Resistance	R	Ohm (\(\Omega\))
Impedance	Z	Ohm (\(\Omega\))
Reactive Power	Q	VAR

🔂 AC Waveform Characteristics

RMS (Root Mean Square) Values:

\[V_{rms} = \frac{V_m}{\sqrt{2}} \approx 0.707 \times V_m\] \[I_{rms} = \frac{I_m}{\sqrt{2}} \approx 0.707 \times I_m\]

Average Value (for half cycle of sine wave):

\[V_{avg} = \frac{2 V_m}{\pi} \approx 0.637 \times V_m\] \[I_{avg} = \frac{2 I_m}{\pi} \approx 0.637 \times I_m\]

Form Factor:

\[\text{Form Factor} = \frac{V_{rms}}{V_{avg}} \approx 1.11\]

Peak Factor (Crest Factor):

\[\text{Peak Factor} = \frac{V_m}{V_{rms}} \approx 1.414\]

Quantity	Symbol	Unit
Peak Voltage	\(V_m\)	Volt (V)
Peak Current	\(I_m\)	Ampere (A)
RMS Voltage	\(V_{rms}\)	Volt (V)
RMS Current	\(I_{rms}\)	Ampere (A)
Average Voltage	\(V_{avg}\)	Volt (V)
Average Current	\(I_{avg}\)	Ampere (A)
Form Factor	-	Unitless
Peak Factor	-	Unitless

📐 Impedance and Reactance

\[Z = \sqrt{R^2 + X^2}\] \[X = X_L - X_C\]

Quantity	Symbol	Unit
Impedance	Z	Ohm (\(\Omega\))
Resistance	R	Ohm (\(\Omega\))
Total Reactance	X	Ohm (\(\Omega\))
Inductive Reactance	\(X_L\)	Ohm (\(\Omega\))
Capacitive Reactance	\(X_C\)	Ohm (\(\Omega\))

🌀 Inductive & Capacitive Reactance

\[X_L = 2\pi f L\] \[X_C = \frac{1}{2\pi f C}\]

Quantity	Symbol	Unit
Inductive Reactance	\(X_L\)	Ohm (\(\Omega\))
Capacitive Reactance	\(X_C\)	Ohm (\(\Omega\))
Frequency	f	Hertz (Hz)
Inductance	L	Henry (H)
Capacitance	C	Farad (F)

⚙️ Admittance

\[Y = \frac{1}{Z}\]

Quantity	Symbol	Unit
Admittance	Y	Siemens (S) or mho (\(\mho\))
Impedance	Z	Ohm (\(\Omega\))

🔋 Capacitance

\[C = \frac{\varepsilon_0 \varepsilon_r A}{d}\]

Quantity	Symbol	Unit
Capacitance	C	Farad (F)
Permittivity of Free Space	\(\varepsilon_0\)	Farad/meter (F/m) \(\approx 8.854 \times 10^{-12}\) F/m
Relative Permittivity (Dielectric Constant)	\(\varepsilon_r\)	Unitless
Area of Plates	A	Meter² (m²)
Distance between Plates	d	Meter (m)

🔄 Transformer Formulas

Voltage and Turns Ratio:

\[\frac{V_1}{V_2} = \frac{N_1}{N_2}\]

Current and Turns Ratio (for Ideal Transformer):

\[\frac{I_2}{I_1} = \frac{N_1}{N_2}\]

Quantity	Symbol	Unit
Primary Voltage	\(V_1\)	Volt (V)
Secondary Voltage	\(V_2\)	Volt (V)
Primary Turns	\(N_1\)	Unitless
Secondary Turns	\(N_2\)	Unitless
Primary Current	\(I_1\)	Ampere (A)
Secondary Current	\(I_2\)	Ampere (A)

📐 Constants & Conversions

Quantity	Value	Unit
1 Kilowatt-hour (kWh)	1000 Wh = 3,600,000 J	Energy
1 Horsepower (HP)	746 W (Electrical HP)	Power
Speed of Light (in vacuum)	\(3 \times 10^8\)	m/s
Permittivity of free space	\(8.854 \times 10^{-12}\)	F/m
Permeability of free space	\(4\pi \times 10^{-7}\)	H/m

⚙️ Efficiency of Electrical Machines

\[\eta = \frac{\text{Output Power}}{\text{Input Power}} \times 100\%\]

Quantity	Symbol	Unit
Efficiency	\(\eta\)	Percent (%)
Output Power	-	Watt (W)
Input Power	-	Watt (W)

Applies to motors, transformers, generators, etc.

Battery Efficiency

\[\eta = \frac{\text{Output Energy}}{\text{Input Energy}} \times 100\%\]

Quantity	Symbol	Unit
Efficiency	\(\eta\)	Percent (%)
Output Energy	-	Watt-hour (Wh)
Input Energy	-	Watt-hour (Wh)

⏱ Frequency & Time Period

\[f = \frac{1}{T}\]

Quantity	Symbol	Unit
Frequency	f	Hertz (Hz)
Time Period	T	Second (s)