7.3 Electrical Components: Resistors, Capacitors, Inductors & Transformers

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7.1 Electrical Principles: Voltage, Current, Resistance & Ohm's Law (V=IR, P=VI) 7.2 Electric Circuits: Series, Parallel & Combination Circuit Analysis 7.3 Electrical Components: Resistors, Capacitors, Inductors & Transformers 7.4 Electronic Semiconductors, Transistors, Diodes & Logic Gates

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7.3 Electrical Components: Resistors, Capacitors, Inductors & Transformers

Key Takeaways Explain This Topic AI

Resistors limit current flow and are color-coded with 4-band or 5-band color rings to indicate resistance value, multiplier, and tolerance.

Capacitors store electrical energy in an electrostatic field between conductive plates, oppose rapid changes in voltage, and block DC while passing AC.

Inductors store electrical energy in a magnetic field within wire coils, oppose rapid changes in current (Lenz's Law), and block high-frequency AC while passing DC.

Transformers transfer AC electrical energy between circuits via mutual electromagnetic induction, stepping voltage up or down proportional to the turns ratio (V_p / V_s = N_p / N_s).

Total AC opposition to current flow is called Impedance (Z), combining resistance (R) and frequency-dependent reactances (X_C and X_L). Last updated: July 2026

7.3 Electrical Components: Resistors, Capacitors, Inductors & Transformers Quick Answer: Electronic circuits rely on fundamental passive components : Resistors limit current and drop voltage; Capacitors store charge in electrostatic fields and oppose voltage changes; Inductors store energy in magnetic fields and oppose current changes; and Transformers step AC voltage up or down using mutual electromagnetic induction. Mastering resistor color codes, component reactance ( X C , X L X_C, X_L X C , X L ), and transformer turns ratios ( N p / N s N_p/N_s N p / N s ) is useful for Electronics Information practice. 1. Passive vs. Active Components Overview Passive Components: Electrical components that cannot generate energy or amplify power. They store, dissipate, or release electrical energy (e.g., Resistors, Capacitors, Inductors, Transformers). Active Components: Components that rely on an external power source to control electric current, amplify signals, or perform switching functions (e.g., Transistors, Diodes, Integrated Circuits). 2. Resistors & Color Coding Systems Resistors are designed to provide a specific amount of electrical resistance in a circuit. They are rated by two primary specifications: Resistance Value (Ohms, Ω \Omega Ω ): The opposition to current. Power Rating (Watts, W W W ): The maximum power the resistor can safely dissipate as heat without burning out ( 1 / 8 W , 1 / 4 W , 1 / 2 W , 1 W , 5 W 1/8\text{W}, 1/4\text{W}, 1/2\text{W}, 1\text{W}, 5\text{W} 1/8 W , 1/4 W , 1/2 W , 1 W , 5 W ). Physical size determines wattage rating, not resistance value! [ 4-Band Resistor Color Code Guide ]

+-------------------------------------------------+ | [Band 1] [Band 2] [Band 3] [Band 4] | | 1st Digit 2nd Digit Multiplier Tolerance | +-------------------------------------------------+ The Standard Resistor Color Code Table

Color Digit (Bands 1 & 2) Multiplier (Band 3) Tolerance (Band 4) Black 0 10 0 = 1 10^0 = 1 1 0 0 = 1 - Brown 1 10 1 = 10 10^1 = 10 1 0 1 = 10 ± 1 % \pm 1\% ± 1% Red 2 10 2 = 100 10^2 = 100 1 0 2 = 100 ± 2 % \pm 2\% ± 2% Orange 3 10 3 = 1 , 000 10^3 = 1,000 1 0 3 = 1 , 000 ( 1 k 1\text{ k} 1 k ) - Yellow 4 10 4 = 10 , 000 10^4 = 10,000 1 0 4 = 10 , 000 - Green 5 10 5 = 100 , 000 10^5 = 100,000 1 0 5 = 100 , 000 ± 0.5 % \pm 0.5\% ± 0.5% Blue 6 10 6 = 1 , 000 , 000 10^6 = 1,000,000 1 0 6 = 1 , 000 , 000 ( 1 M 1\text{ M} 1 M ) ± 0.25 % \pm 0.25\% ± 0.25% Violet 7 10 7 = 10 , 000 , 000 10^7 = 10,000,000 1 0 7 = 10 , 000 , 000 ± 0.1 % \pm 0.1\% ± 0.1% Grey 8 10 8 10^8 1 0 8 - White 9 10 9 10^9 1 0 9 - Gold - 0.1 0.1 0.1 ± 5 % \pm 5\% ± 5% Silver - 0.01 0.01 0.01 ± 10 % \pm 10\% ± 10% (None) - - ± 20 % \pm 20\% ± 20% classification practice Mnemonic: B ad B oys R ob O ur Y oung G irls B ut V iolet G ives W illingly ( B lack, B rown, R ed, O range, Y ellow, G reen, B lue, V iolet, G rey, W hite). Step-by-Step Color Code Decoding Example Determine the resistance value of a resistor with color bands: Yellow - Violet - Red - Gold . Band 1 (Yellow): First digit = 4 Band 2 (Violet): Second digit = 7 Band 3 (Red): Multiplier = 10 2 = 100 10^2 = 100 1 0 2 = 100 Band 4 (Gold): Tolerance = ± 5 % \pm 5\% ± 5% Calculation: 47 × 100 = 4 , 700 Ω = 4.7 k Ω ± 5 % 47 \times 100 = 4,700\Omega = 4.7\text{ k}\Omega \pm 5\% 47 × 100 = 4 , 700Ω = 4.7 k Ω ± 5% . Tolerance Range: 4 , 700 × 0.05 = 235 Ω ⟹ 4 , 465 Ω to 4 , 935 Ω 4,700 \times 0.05 = 235\Omega \implies 4,465\Omega \text{ to } 4,935\Omega 4 , 700 × 0.05 = 235Ω ⟹ 4 , 465Ω to 4 , 935Ω . 3. Capacitors & Capacitance ( C C C ) A Capacitor is an electrical component consisting of two parallel conductive plates separated by an insulating material called a dielectric (e.g., Air, Ceramic, Mica, Electrolytic, Mylar). [ Capacitor Physical Construction ]

Plate 1 (Conductive) ----+ +---- Lead 1 | | DIELECTRIC INSULATOR -->|| <-- Electrostatic Field | | Plate 2 (Conductive) ----+ +---- Lead 2 Core Properties of Capacitors: Capacitance Formula: C = Q V C = \frac{Q}{V} C = V Q (measured in Farads, F ; practical units are μ F \mu\text{F} μ F , nF \text{nF} nF , pF \text{pF} pF ). Energy Stored: Stores energy in an electrostatic field : E = 1 2 C V 2 E = \frac{1}{2} C V^2 E = 2 1 C V 2 . Behavior: Opposes sudden changes in voltage ( I = C d V d t I = C \frac{dV}{dt} I = C d t d V ). DC vs AC: Blocks DC (after charging to full source voltage) and passes AC signals. Capacitors in Series and Parallel (Opposite of Resistors!) Parallel Capacitors: Total capacitance increases (increases total plate surface area): C Total = C 1 + C 2 + C 3 + ⋯ + C n C_{\text{Total}} = C_1 + C_2 + C_3 + \dots + C_n C Total = C 1 + C 2 + C 3 + ⋯ + C n Series Capacitors: Total capacitance decreases (increases effective dielectric thickness): 1 C Total = 1 C 1 + 1 C 2 + … ⟹ C Total = C 1 × C 2 C 1 + C 2 \frac{1}{C_{\text{Total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots \quad \implies \quad C_{\text{Total}} = \frac{C_1 \times C_2}{C_1 + C_2} C Total 1 = C 1 1 + C 2 1 + … ⟹ C Total = C 1 + C 2 C 1 × C 2 Capacitive Reactance ( X C X_C X C ) Capacitive Reactance is the opposition a capacitor offers to alternating current, measured in Ohms ( Ω \Omega Ω ): X C = 1 2 π f C X_C = \frac{1}{2 \pi f C} X C = 2 π f C 1 As AC frequency ( f f f ) increases , capacitive reactance ( X C X_C X C ) decreases . At 0 Hz 0\text{ Hz} 0 Hz (DC), X C = ∞ Ω X_C = \infty \Omega X C = ∞Ω (Open Circuit). 4. Inductors & Inductance ( L L L ) An Inductor (also called a coil, choke, or reactor) consists of a conductive wire wrapped around a core (air, iron, or ferrite). Core Properties of Inductors: Inductance ( L L L ): Measured in Henries (H) (or mH \text{mH} mH , μ H \mu\text{H} μ H ). Energy Stored: Stores electrical energy in a magnetic field : E = 1 2 L I 2 E = \frac{1}{2} L I^2 E = 2 1 L I 2 . Lenz's Law & Back-EMF: Inductors oppose any change in current by inducing a counter-voltage (back-EMF). DC vs AC: Passes DC easily (offering only wire resistance) and blocks high-frequency AC . Inductors in Series and Parallel (Same as Resistors!) Series Inductors: L Total = L 1 + L 2 + L 3 + ⋯ + L n L_{\text{Total}} = L_1 + L_2 + L_3 + \dots + L_n L Total = L 1 + L 2 + L 3 + ⋯ + L n Parallel Inductors: 1 L Total = 1 L 1 + 1 L 2 + … \frac{1}{L_{\text{Total}}} = \frac{1}{L_1} + \frac{1}{L_2} + \dots L Total 1 = L 1 1 + L 2 1 + … Inductive Reactance ( X L X_L X L ) Inductive Reactance is the opposition an inductor offers to alternating current, measured in Ohms ( Ω \Omega Ω ): X L = 2 π f L X_L = 2 \pi f L X L = 2 π f L As AC frequency ( f f f ) increases , inductive reactance ( X L X_L X L ) increases directly.

Loading diagram... Transformer Voltage and Current Step-Down Relationships

5. Transformers & Electromagnetic Induction A Transformer is a static electrical device that transfers electrical energy between two or more AC circuits through mutual electromagnetic induction . [ Ideal Transformer Schematic ]

Primary Coil (Np) Iron Core Secondary Coil (Ns) ---( )--- || ---( )--- Vp AC ---( )--- || ---( )--- Vs AC ---( )--- || ---( )--- The Transformer Equations: Turns & Voltage Ratio: V p V s = N p N s \text{Turns \& Voltage Ratio: } \frac{V_p}{V_s} = \frac{N_p}{N_s} Turns & Voltage Ratio: V s V p = N s N p Power Conservation (Ideal 100% Efficient): P Primary = P Secondary ⟹ V p × I p = V s × I s \text{Power Conservation (Ideal 100\% Efficient): } P_{\text{Primary}} = P_{\text{Secondary}} \implies V_p \times I_p = V_s \times I_s Power Conservation (Ideal 100% Efficient): P Primary = P Secondary ⟹ V p × I p = V s × I s Current Inverse Ratio: I s I p = N p N s = V p V s \text{Current Inverse Ratio: } \frac{I_s}{I_p} = \frac{N_p}{N_s} = \frac{V_p}{V_s} Current Inverse Ratio: I p I s = N s N p = V s V p Types of Transformers: Step-Down Transformer: N s < N p ⟹ V s < V p N_s < N_p \implies V_s < V_p N s < N p ⟹ V s < V p (Voltage decreases, Current increases). Step-Up Transformer: N s > N p ⟹ V s > V p N_s > N_p \implies V_s > V_p N s > N p ⟹ V s > V p (Voltage increases, Current decreases). Isolation Transformer: N s = N p ⟹ V s = V p N_s = N_p \implies V_s = V_p N s = N p ⟹ V s = V p (Used to decouple grounded circuits for safety). Transformer Calculation Worked Example A step-down power transformer has 1 , 200 turns 1,200\text{ turns} 1 , 200 turns on its primary winding and 100 turns 100\text{ turns} 100 turns on its secondary winding. If 120 V AC 120\text{V AC} 120 V AC is applied across the primary coil, find the secondary voltage ( V s V_s V s ). Formula: V p V s = N p N s ⟹ V s = V p × ( N s N p ) \frac{V_p}{V_s} = \frac{N_p}{N_s} \implies V_s = V_p \times \left( \frac{N_s}{N_p} \right) V s V p = N s N p ⟹ V s = V p × ( N p N s ) Calculation: V s = 120 V × ( 100 1 , 200 ) = 120 × 1 12 = 10.0 Volts AC V_s = 120\text{V} \times \left( \frac{100}{1,200} \right) = 120 \times \frac{1}{12} = 10.0\text{ Volts AC} V s = 120 V × ( 1 , 200 100 ) = 120 × 12 1 = 10.0 Volts AC . 6. Comprehensive Passive Component Summary Reference Table

Component Symbol Unit Energy Storage Mechanism AC Behavior DC Behavior Resistor R R R Ohm ( Ω \Omega Ω ) Dissipates energy as heat Opposes AC ( R R R ) independent of frequency Opposes DC ( R R R ) Capacitor C C C Farad (F) Stores energy in Electrostatic field Passes AC ( X C = 1 2 π f C X_C = \frac{1}{2\pi f C} X C = 2 π f C 1 ) Blocks DC ( X C = ∞ X_C = \infty X C = ∞ ) Inductor L L L Henry (H) Stores energy in Magnetic field Blocks AC ( X L = 2 π f L X_L = 2\pi f L X L = 2 π f L ) Passes DC ( X L = 0 X_L = 0 X L = 0 ) Transformer T T T Ratio ( N p : N s N_p:N_s N p : N s ) Mutual Magnetic Flux coupling Steps V V V and I I I up/down Does NOT operate on DC

Test Your Knowledge

What is the resistance and tolerance of a 4-band resistor with the color bands: RED - VIOLET - ORANGE - GOLD?

27,000 Ohms ± 5%

2,700 Ohms ± 10%

270 Ohms ± 5%

270,000 Ohms ± 20% Check Answer Need a hint? AI

Test Your Knowledge

Two capacitors rated at 10 Microfarads (µF) and 15 Microfarads (µF) are connected in PARALLEL. What is their combined total capacitance?

6.0 Microfarads

25.0 Microfarads

150.0 Microfarads

12.5 Microfarads Check Answer Need a hint? AI

Test Your Knowledge

A transformer has a primary winding of 800 turns and a secondary winding of 200 turns. If the primary side is connected to a 120V AC source, what is the output voltage on the secondary side?

480 Volts AC

240 Volts AC

30 Volts AC

60 Volts AC Check Answer Need a hint? AI

Test Your Knowledge

What happens to the inductive reactance (XL) of an inductor as the frequency of an AC signal INCREASES?

Inductive reactance decreases toward zero

Inductive reactance remains completely unchanged

Inductive reactance drops by half

Inductive reactance increases proportionally Check Answer Need a hint? AI

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