JNTU B.Tech II Year ELECTRICAL AND ELECTRONICS ENGINEERING Previous Question Paper (October - 2020 - R13)

Kirchhoff's laws are fundamental laws used to analyze electrical circuits. There are two laws:

Kirchhoff's Current Law (KCL) or Junction Rule: This law states that the algebraic sum of currents entering any junction (or node) in an electrical circuit is equal to the algebraic sum of currents leaving that junction. Mathematically, it can be expressed as:

This law is based on the principle of conservation of charge. At a junction, charge cannot accumulate, so the rate at which charge enters must equal the rate at which it leaves.

Kirchhoff's Voltage Law (KVL) or Loop Rule: This law states that the algebraic sum of all the voltage drops around any closed loop in an electrical circuit is equal to the algebraic sum of all the voltage rises in that loop. Mathematically, it can be expressed as:

This law is based on the principle of conservation of energy. As a charge traverses a closed loop and returns to its starting point, the net work done on it by the electric field must be zero, meaning the net change in potential energy is zero.

A Permanent Magnet Moving Coil (PMMC) instrument is an instrument used for measuring direct current (DC) and voltage. It operates on the principle that a current-carrying conductor placed in a magnetic field experiences a mechanical force.

Working Principle:

When a current flows through a coil placed in the magnetic field produced by a permanent magnet, the coil experiences a torque. This torque causes the coil to rotate. The magnitude of this torque is directly proportional to the current flowing through the coil.

Construction:

A PMMC instrument typically consists of the following main parts:

• Permanent Magnet: Provides a uniform radial magnetic field.
• Moving Coil: A lightweight coil wound on a former, pivoted on jewel bearings, and free to rotate within the magnetic field. It carries the current to be measured.
• Control Springs: Usually two phosphor bronze hair springs are used. They provide the controlling torque, which opposes the deflecting torque and also serve as the means for leading the current into and out of the moving coil.
• Pointer: Attached to the moving coil, it moves over a calibrated scale to indicate the measured value.
• Damper: Usually an aluminum former on which the moving coil is wound. Eddy currents induced in this former during rotation provide damping, preventing excessive oscillation.

Diagram:

(A neat diagram would show a U-shaped permanent magnet with pole pieces, a pivoted rectangular coil placed in the air gap, control springs attached to the coil, and a pointer attached to the coil moving over a scale. Arrows would indicate the magnetic field lines and the direction of current flow.)

Working:

When a DC current to be measured is passed through the moving coil, it produces a magnetic field that interacts with the field of the permanent magnet. This interaction generates a deflecting torque (T_d) given by:

where:

N = number of turns in the coil

I = current flowing through the coil

A = area of the coil

B = magnetic flux density of the permanent magnet

The control springs exert a controlling torque (T_c) which is proportional to the angle of deflection (θ):

where k is the spring constant.

For a steady deflection, the deflecting torque equals the controlling torque:

Therefore, the deflection angle θ is directly proportional to the current I:

This linear relationship between deflection and current makes PMMC instruments ideal for ammeters and voltmeters. The scale is uniform.