Explain briefly the workings of electrical transformer, both step-up and step-down

In a step-up transformer, compare the secondary voltage and current to the corresponding primary values. Explain briefly how transformers minimize losses in long distance electrical circuits.

What is the relationship between kWh and Joules?

Explain briefly the difference between peaks and rms voltage.

In an AC circuit that contains a capacitor and an inductor, impedance replaces the DC concept of resistance. Explain briefly the difference between the two quantities.

An AC circuit with a variable frequency generator, a resistor, an inductor, and a capacitor has a resonant frequency, at which the maximum current flows. Explain

1. The step-down transformer reduces the

primary voltage by a factor equal to the
turns ratio. For instance, if the turns ratio was 4:1, the voltage across the secondary would be 1/4 of the primary voltage. In a step-up transformer with
a turns-ratio of 1:4, the voltage across
the secondary would be four times the
primary voltage.

2. In a step-up transformer with a turns-ratio of 1:4, the secondary voltage will be 4 times the primary voltage. The secondary current will be
1/4 of the primary current.

In long distance electrical circuits, the step-up transformer is used to reduce the line current which reduces
the I^2*R losses.

3. 1kW = 1KJ/s
1kWh = 1KJ/s*3600s
1kWh = 3600kJ

4. rms means root-mean-square and is 0.707 times the peak value.

5. The impedance of a circuit is the ratio of the applied rms voltage to the
resulting rms current(Vrms/Irms).

The D.C. resistance is the ratio of the applied D.C. voltage to the resulting D.C. current(Vdc/Idc).

6. At the resonant frequency, the reactance of the inductor and capacitor
are equal and opposite. Therefore. the
net reactance is zero. So the current is
maximized and determined by the value of
the resistor.

In a step-up transformer, the secondary voltage is higher than the primary voltage, while the secondary current is lower than the primary current. This is achieved by having more turns in the secondary coil than in the primary coil. The transformer works on the principle of electromagnetic induction. When an alternating current (AC) flows through the primary coil, it creates a time-varying magnetic field. This magnetic field induces an alternating voltage in the secondary coil, which can be stepped up or down based on the number of turns in the coils.

Transformers minimize losses in long-distance electrical circuits through several mechanisms. Firstly, transformers operate at high voltages to reduce current since power loss is proportional to the square of the current. This allows for more efficient transmission of power over long distances. Secondly, transformers are designed with high-quality materials and efficient insulation to minimize energy losses through heat dissipation. Additionally, transformers are often operated at specific frequencies to match the characteristics of the electrical power system, further maximizing the efficiency of power transmission.

The relationship between kWh (kilowatt-hour) and Joules is based on the conversion factor of 1 kWh = 3.6 x 10^6 Joules. Kilowatt-hour is a unit of energy commonly used in electricity billing, representing the amount of energy consumed by a device with a power of 1 kilowatt over a period of one hour. Joule, on the other hand, is the standard derived unit of energy in the International System of Units (SI). To convert from kilowatt-hours to Joules, you can multiply the value in kWh by 3.6 x 10^6.

Peaks voltage refers to the maximum value reached by an alternating voltage during one complete cycle, while rms (root mean square) voltage represents the effective or average voltage of an alternating signal. Peaks voltage is the actual magnitude of the voltage waveform and is useful for determining the maximum potential stress on equipment. On the other hand, rms voltage takes into account the time-varying nature of the waveform and is often used to calculate power or compare voltage levels consistently.

In an AC circuit that contains a capacitor and an inductor, impedance replaces the concept of resistance in DC circuits. Impedance is a measure of the opposition or resistance to the flow of alternating current in a circuit. It consists of two components: resistance (R) and reactance (X), where reactance can be either inductive (XL) or capacitive (XC) depending on the type of element in the circuit. The main difference between impedance and resistance is that impedance considers the effects of both resistive and reactive elements in the circuit. While resistance resists the flow of both AC and DC currents equally, reactance changes with frequency and can either enhance or impede the flow of AC current.

In an AC circuit with a variable frequency generator, resistor, inductor, and capacitor, a resonant frequency exists at which the maximum current flows. This resonant frequency occurs when the inductive reactance and capacitive reactance in the circuit cancel each other out, resulting in a minimum impedance. At the resonant frequency, the impedance is purely resistive, and the circuit is said to be in resonance. This leads to a maximum flow of current as the circuit is effectively in a state of minimum opposition to the AC current. Resonance is an important concept in AC circuits and is utilized in various applications such as tuning circuits and filters.