Electrical circuits consist of three fundamental passive components: Resistance (R), Capacitance (C), and Inductance (L). These elements define how electrical energy is dissipated, stored, or transferred in a circuit. We are going to discuss an overview of each element in this blog post.
Electric Resistance:
Symbol:
Mathematical Relation
- V = IR (Where V is voltage, I is current, and R is resistance.)
- R=ρL/A (where L is the length of the conductor, A is the area of conductor, ρ is the resistivity of the conductor)
Resistivity(ρ) depends on the Properties of material.Behavior:
- Converts electrical energy into heat.
- Linear element: Voltage and current are directly proportional.
- Resistance has properties of temperature coefficient one is a negative coefficient of temperature while another is a positive coefficient of temperature. The negative coefficient of the temperature of the conductor is defined as the resistance decreased with increased temperature, while the positive coefficient of the temperature of the conductor is defined as the resistance increased with increased temperature
Capacitance:
Definition: Capacitance is the ability of a component to store electrical energy in an electric field.- It consists of two metallic surfaces separated by an insulating material such as wood, plastics, rubber etc, this insulating material is called the DIELECTRIC.
Symbol: C
Mathematical Relation:
The capacitor is charged by connecting one plate and another plate to the cathode by the terminal of the battery or, Active element then the electric field produced by the active source (Battery) cause to flow toward the positive terminal of the active source (Battery) and away from the negative terminal. This is caused by charging in a capacitor.
Inductance:
- Temporarily stores energy in a magnetic field.
- Allows DC to pass (acts as a short circuit in steady-state DC) and opposes sudden changes in AC.
Comparison of R, L, and C:
Parameter | Resistance (R) | Capacitance (C) | Inductance (L) |
Physical Property | Opposition to current flow (friction in electrons). | Ability to store energy in an electric field. | Ability to store energy in a magnetic field. |
Energy | Dissipates as heat. | Stores energy temporarily (electric). | Stores energy temporarily (magnetic). |
Impedance (AC) | Constant (R) | Z=1/jωC | Z=jωL |
Frequency Behavior | Independent of frequency. | Impedance decreases with frequency | Impedance increases with frequency |
Reactance | None (purely resistive). | XC=1/ωC | XL=ωL |
Phase Relationship | Voltage and current are in phase. | Current leads voltage by 90∘ | Voltage leads current by 90∘ |
Power Consume | Real power is dissipated. | No real power consumption; only reactive power is exchanged. | No real power consumption; only reactive power is exchanged. |
Unit | Ohms | Farads | Henry |
Symbol | R | C | L |
Response to DC | Constant resistance | Acts as an open circuit. | Acts as a short circuit. |
Response to AC | Same resistance as DC. | Impedance decreases with frequency | Impedance increases with frequency |
Transient Response | Instantaneous response. | Exponential charge and discharge curves. | Exhibits time lag due to energy buildup in the magnetic field. |
Waveform Behavior | Does not affect waveform shape. | Affects the amplitude and phase of AC signals. | Affects amplitude and phase of AC signals. |
Applications | Voltage dividers, heaters, etc. | Filters, oscillators, and energy storage. | Transformers, motors, and oscillators |
📝 Multiple Choice Questions (MCQs) on Resistance, Capacitance, and Inductance
1. Which of the following is the correct unit of resistance?
A) Farad (F)
B) Ohm (Ω)
C) Henry (H)
D) Siemens (S)
Answer: B) Ohm (Ω)
Explanation: Resistance is measured in ohms (Ω), which defines opposition to the flow of current.
2. Resistance of a conductor depends on which of the following?
A) Length of conductor
B) Cross-sectional area
C) Material resistivity
D) All of the above
Answer: D) All of the above
Explanation: Resistance , hence depends on length (L), area (A), and resistivity (ρ).
3. The opposition offered by a capacitor to AC is known as:
A) Inductive reactance
B) Capacitive reactance
C) Impedance
D) Resistance
Answer: B) Capacitive reactance
Explanation: Capacitive reactance is given by , which decreases with frequency.
4. What happens to a capacitor in steady-state DC conditions?
A) Acts as a short circuit
B) Acts as an open circuit
C) Stores infinite energy
D) Becomes resistive
Answer: B) Acts as an open circuit
Explanation: In steady-state DC, the capacitor gets fully charged and blocks further current, behaving like an open circuit.
5. Inductance is measured in:
A) Weber (Wb)
B) Volt-second
C) Henry (H)
D) Tesla (T)
Answer: C) Henry (H)
Explanation: The SI unit of inductance is Henry (H), which represents the ability to store energy in a magnetic field.
6. In an inductor, the voltage:
A) Lags current by 90°
B) Leads current by 90°
C) In phase with current
D) Independent of current
Answer: B) Leads current by 90°
Explanation: In inductors, voltage leads current by 90° due to magnetic energy storage.
7. Which component dissipates real power as heat?
A) Resistance
B) Capacitance
C) Inductance
D) None
Answer: A) Resistance
Explanation: Only resistors consume real power (P = I²R), while capacitors and inductors exchange reactive power.
8. What is the behavior of inductive reactance () with frequency?
A) Increases with frequency
B) Decreases with frequency
C) Remains constant
D) Zero always
Answer: A) Increases with frequency
Explanation: , so inductive reactance increases linearly with frequency.
9. Which passive element stores energy in an electric field?
A) Resistance
B) Inductance
C) Capacitance
D) None
Answer: C) Capacitance
Explanation: Capacitors store energy in the electric field between their plates.
10. In a pure resistive circuit, the phase difference between voltage and current is:
A) 0°
B) 45°
C) 90°
D) 180°
Answer: A) 0°
Explanation: In resistors, voltage and current are in the same phase, unlike in capacitors and inductors.