Geometry and Algebra Questions for 10th Class

Basic Electric System

• A circuit is a closed path for electric current flow.
• Circuits are composed of active and passive elements.
• Active elements supply energy (e.g., batteries, generators).
• Conductors carry current (e.g., wires).
• Loads utilize electrical energy (e.g., bulbs, fans).
• Safety devices protect the circuit (e.g., fuses, circuit breakers).
• Controlling devices regulate current flow (e.g., switches).

Current Flow in a Circuit

• Electric current is the rate of electric charge flow.
• The unit of electric current is the ampere (A).
• Current flow occurs due to the movement of free electrons in a conductor.
• Current is directly proportional to the drift velocity, the number of free electrons, the cross-sectional area, and the charge of electrons in the conductor.
• Current = (charge of each electron) x (number of electrons per unit volume) x (drift velocity) x (cross-sectional area)

Coulomb

• The rate of flow of electric charge is electric current.
• The unit of electric charge is Coulomb
• Electromotive force (EMF) is the energy per unit charge supplied by a source.
• EMF is measured in volts.
• EMF is not a force but energy provided to charge by active components like batteries.
• The potential difference between two points is the amount of work done in moving a unit charge between the two points.

Potential Difference

• Potential difference between two points is commonly referred to as voltage.
• The unit of potential difference is volts (V).
• EMF maintains potential difference.
• Potential difference causes current flow.
• The potential difference between two charged bodies is called potential difference
• When two bodies have different electric potentials, a potential difference exists between them.

Electrical Units

• Electric current: Ampere (A)
• Potential difference: Volt (V)
• Power: Watt (W)
• Resistance: Ohm (Ω)
• Capacitance: Farad (F)
• Inductance: Henry (H)

Passive Components

• Passive components do not generate power; they dissipate, store, or release it.
• Examples include resistors, capacitors, and inductors.
• Active components require an external power source.

Source

• Independent sources (voltage and current sources) don't depend on other circuit quantities, but depend on the source itself
• There are two types of independent sources; voltage and current sources.
• Voltage source maintains a constant voltage irrespective of the current flowing through it.
• Current source maintains a constant current irrespective of the voltage across it.

Voltage Source vs. Current Source

• Ideal voltage source: Maintains constant voltage across its terminals, regardless of load current.
• Practical voltage source: Output voltage decreases as load current increases due to internal resistance.
• Ideal current source: Maintains constant current through its terminals, regardless of load voltage.

Current Source vs. Practical Current Source

• Ideal current source: Output current remains constant, regardless of load voltage.
• Practical current source: Output current decreases as load resistance decreases due to internal resistance.

Source Transformation

• Converting a voltage source to a current source or vice-versa.

Ohm's Law

• Current is directly proportional to voltage and inversely proportional to resistance.
• I = V/R

Temperature Coefficient of Resistance

• The amount of change in resistance with a change in temperature.
• Metals typically have a positive temperature coefficient, meaning their resistance increases with temperature increase.
• Alloys, electrolytes, mica, and rubber have negative temperature coefficients.

DC Circuits and Network Theorems

• DC circuits involve direct current flowing continuously in a single direction
• Network Theorems describe relationships between voltages, currents, and resistances in circuits.

AC (Alternating Current)

• Ac is a current that continuously reverses direction.
• AC waveform shows variations over time.
• Various ways to represent AC quantities are peak value, Rms value, and instantaneous value.

Phase

• Phase difference, in an AC circuit, is the difference in the starting times of a given voltage or current wave relative to another wave having a reference or starting point or zero stage
• When two quantities are 90 degrees out of phase, one is said to lead the other or lag
• In phase means no difference in phase

Power in AC circuit

• Active power: Is also called True Power or Real Power. It is responsible for the useful power in the circuit, measured in watts (W).
• Reactive power: It is responsible for the development and maintenance of electromagnetic fields within an AC circuit. Usually given in VARS or Reactive Volt-Amperes.
• Apparent power: It is the product of the voltage and current in an AC circuit. Usually given in VA or Volt-Amperes.

Power Factor

• The ratio of active power to apparent power.
• It is used to determine how effectively energy is being delivered to a load, in an AC circuit.
• A power factor of 1 indicates maximum effectiveness.

Power Factor in Industrial Facilities

• Industrial facilities often have a lagging power factor, meaning the current lags behind the voltage.
• Capacitors can be used to compensate for this lagging effect.

Semiconductor Devices (Diodes, Transistors)

• Semiconductor materials exhibit electrical conductivity between that of a conductor and an insulator.
• Diodes: Two-terminal devices that conduct current primarily in one direction. Various types exist (e.g., Zener, Varactor, LED, Photodiode).
• Transistors: Three-terminal devices that act as amplifiers or switches. P-N-P or N-P-N types, work in various modes (active, saturated, cut-off, inverted). Transistors are commonly used in amplifier circuits and digital circuit implementations.

Circuit Configurations and Theorems

• Series: Components connected end-to-end, each component carrying identical current.
• Parallel: Components connected across each other, each component carrying identical voltage.
• Thevenin's Theorem: A complex two-terminal network can be replaced by an equivalent voltage source and series resistance, to measure load current.
• Norton's Theorem: A complex two-terminal network can be replaced by an equivalent current source and parallel resistance, to measure load current.
• Superposition Theorem: The overall effect of multiple sources can be calculated by analyzing each source separately and then adding the individual effects.
• Reciprocity Theorem: If the excitation (e.g., voltage or current source) in one branch of a bilaterally linear network is replaced with a response in another branch, then the reverse interchange of excitation and response produces identical effects.

Maximum Power Transfer

• Maximum power is transferred to the load when the load resistance equals the thevenin resistance.

Test your knowledge of geometry and algebra with this quiz designed for 10th class students. Questions include topics such as the area of a rectangle, the Pythagorean theorem, simplifying expressions, arithmetic sequences, and properties of parallel lines. Challenge yourself and see how well you understand these fundamental concepts!