NARAYANKAR NOTES

  Gravity is the force that pulls objects towards the Earth (or any planet). Gravitation is the general force of attraction between any two objects in the universe. Simple difference: Gravity = attraction towards Earth . Gravitation = attraction between any two masses (like Earth and Moon, Sun and Earth, etc.). 1. What are the effects of a force acting on an object? When a force is applied to an object, it can cause one or more of the following effects: Change in motion : If the object was not moving, force can make it start moving. Change in speed : If the object is already moving, force can make it move faster or slower. Change in direction : A moving object can change its direction when a force acts on it. Change in shape or size : For example, when you press a sponge, it gets compressed. Stop a moving object : Like when you use brakes on a bicycle. In short : A force can start , stop , speed up , slow down , change direction , or change th...

Continuity Equation (Appeared:  May 2022, May 2023, Dec 2023) The Continuity Equation is a mathematical expression that describes the conservation of electric charge in a semiconductor or conducting medium. It ensures that charge doesn't magically appear or disappear—what goes in must come out unless it is stored or lost. Concept Overview In telecommunication circuits and semiconductor devices like diodes and transistors: Electrons and holes are moving. Their movement creates current. The density of charge in a region may change with time. This change is captured by the continuity equation. General Statement The Continuity Equation is: ∂ρ/∂t + ∇ · J = 0 Where: ρ = charge density (C/m³) ∂ρ/∂t = rate of change of charge density with time ∇ · J = divergence of current density J (A/m²) J = current density vector Physical Meaning If more current leaves a region than enters, charge inside decreases → ∂ρ/∂t becomes negative. If charge b...