DMRC JE Electrical 2014 Paper With Solution and Explanation

Let there be 2 node J₁ and J₂

Now we will first solve Node J2

The 3 resistor i.e 200Ω, 400Ω,  200Ω are connected in series therefore its equivalent resistance is

200Ω + 400Ω + 200Ω = 800Ω

Now two 800Ω resistor are connected in parallel

therefore equivalent resistance is = (800 x 800)/(800 + 800) = 400Ω

Now again from the above circuit diagram

200Ω, 400Ω,  200Ω are connected in series, therefore, its equivalent resistance is

200Ω + 400Ω + 200Ω = 800Ω

Now total equivalent resistance of the circuit will be

400Ω + 100Ω + 100Ω = 600Ω

In most practical cases, you will not see a single amplifier. Rather than you will see a series of the cascaded amplifier. The term cascaded means connected in series. Coupling capacitors are commonly used to connect one amplifier stage to another.

In analog circuits, a coupling capacitor is used to connect two circuits such that only the AC signal from the first circuit can pass through to the next while DC is blocked. This technique helps to isolate the DC bias settings of the two coupled circuits. Capacitive coupling is also known as AC coupling and the capacitor used for the purpose is also known as a DC-blocking capacitor.

Electrolytic Capacitors are generally used in DC power supply circuits due to their large capacitance and small size to help reduce the ripple voltage or for coupling and decoupling applications. Electrolytic’s generally come in two basic forms; Aluminium Electrolytic Capacitors and Tantalum Electrolytic Capacitors. The tantalum and electrolytic capacitors have ratings of 6, 10. 12. 15. 20. 25, 35, 50. 75, 100V, and higher.

Paper capacitors: Paper capacitors use paper as the dielectric. They are made of flat strips of metal foil plates separated by a dielectric, which is usually waxed paper. Paper capacitors have values in the picofarad and low microfarad, ranges. The voltage ratings are usually less than 6 V. Paper capacitors arc usually sealed with wax to prevent moisture problems.

The voltage rating of capacitors is very important. A typical set of values marked on a capacity might be “10 μF, 50 DCWV.” Such a capacitor h a capacitance of 10 μF and a “dc working voltage” of 50V. This means that a voltage in excess of 50 could damage the plates of the capacitors.

Ceramic capacitors: Ceramic capacitors make use of ceramic as the dielectric material. Basically, ceramic materials are fanned from titanium dioxide. Some of the dielectric materials used are barium titanate, magnesium titanic, and sirconium titanate.

Advantages

1. The ceramic capacitor can be made up of any desired size and shape
2. Their capacitance value range from a few pF to nF.
3. They can withstand sufficient high voltage (up to 100 Volts.)

In a computer, term memory is an electronic chip with an integrated circuit that store data.

Generally, there are two types of memory

1. Static
2. Dynamic

Static memory (Non -Volatile memory):  Memory that retains its data without electricity being constantly applied. A static memory uses flip-flops as basic memory cells, to store information. E.G (ROM). A flip-flop that can store one binary bit is called a memory cell. If more than one flip flop is grouped together, it is called a register. One flip-flop to store one bit of information requires 4 to 6 Transistors.

Dynamic memory (Volatile Memory): Memory that does not retain its data unless it is constantly electrically refreshed. In dynamic memories, capacitors are used as the basic storage cells. Since the charge on the capacitors leaks away, we need to refresh this charge Dynamic memories are very much smaller than static ones.  So a dynamic memory device can store information that is approximately four times the information stored in a static device, having the same physical dimension.

A force of attraction exist between two unlike charges whereas a force of repulsion exist between two like charge.

Factors Affecting the Resistance

The resistance R offered by a conductor depends on the following factors :

1. Length of the material (l): The resistance of a material is directly proportional to the length. The resistance of the longer wire is more.
2. Cross-Section Area (a): The resistance of a material is inversely proportional to the cross-sectional area of the material. The more cross-sectional area allowed the passage of more number of electrons offering less resistance.
3. Nature of Material: As discussed earlier the conductor has a large number of free electrons hence it offers less resistance whereas Inductor has less number of free electrons hence it offers more resistance.
4. Temperature: The temperature of the material affects the value of the resistance. In the General case, the resistance of the material increases as its temperature increases.

So for any given material at a certain given temperature, the resistance is given as

where ρ is a constant and known as its specific resistance or resistivity.

l = Length in Meter

a = area of cross-section in m²

R = Resistance in Ohm

Unit of Resistivity

The resistance of all pure metals increases linearly with an increase in temperature over a limited temperature range. At low temperatures, the ions are almost stationary. As the temperature increases, the ions inside the metal acquire energy and start oscillating about their mean positions. This makes it more difficult for the current to flow and causes resistance. These vibrating ions collide with the electrons Hence resistance increases with an increase in temperatures.

Copper comes in the category of pure metal hence its resistance increase with an increase in temperature.

Semiconductor, Insulator, and Electrolyte: The resistance of semiconductors, insulators, and electrolytes (silicon, Glass, Varnish, etc) decreases with an increase in temperature. At zero temperature, the semiconductor behaves as a perfect insulator.  As the temperature increases, some of the electrons acquire energy and become free for conduction. Hence, conductivity increase and resistance decrease with an increase in temperature.

A kilowatt, 1,000 watts, is the unit used to describe the power, the rate at which the energy is being converted. Energy is the power multiplied by time. Therefore a kilowatt-hour, the product of power and time, is a unit c energy. The utility company charges you for the number of kilowatt-hours of electricity you use in a month.

Note watt or kilowatt is the unit of Power.

Joule is the unit of Energy

In the RLC series circuit the total impedance of the series LCR circuit is given as

Z² = R² +  (X₁ – X₂)²

where X₁ is inductive reactance

and X₂ is capacitive reactance.

At a particular frequency (resonant frequency), we find that X₁=X₂ because the resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are 180 degrees apart in phase. Therefore, the phase angle between voltage and current is zero and the power factor is unity.

Thus, at the resonant frequency, the net reactance is zero because of X₁=X₂. The circuit impedance Z becomes minimum and is equal to the resistance R. “Since the impedance is minimum, the current will be maximum”.

Hence electrical resonance is said to take place in a series LCR circuit when the circuit allows maximum current for a given frequency of alternating supply at which capacitive reactance becomes equal to the inductive reactance.

An ideal current source has infinite internal impedance, so when you make its current zero, you are left with an infinite impedance, which is an open circuit.  An ideal current source has the property that it can produce whatever voltage it needs to force its specified current to flow through it

The generator which gives DC supply to the synchronous motor is called as exciter