The question asks for the instrument used to measure electric power. We need to identify the device specifically designed for this purpose and distinguish it from instruments that measure other electrical quantities like voltage, current, or resistance.
Correct Option: C) A Wattmeter is an electrical instrument used to measure electric power (in watts) in a circuit. It has both a current coil (connected in series with the load) and a voltage coil (connected in parallel across the load) to measure both quantities simultaneously and determine their product, which is power.
The question asks about the meaning of a power factor of 1 in an AC circuit. The power factor is a measure of how effectively electrical power is being used in an AC circuit. It is defined as the cosine of the phase angle between the voltage and current.
Definition of Power Factor: The power factor (PF) is given by the formula:
\[ \text{PF} = \cos(\phi) \]where \(\phi\) is the phase angle between the voltage and current in an AC circuit.
Power Factor of 1: If the power factor is 1, then:
\[ \cos(\phi) = 1 \]Determining the Phase Angle: For \(\cos(\phi) = 1\), the phase angle \(\phi\) must be 0 degrees.
Interpretation of Phase Angle: A phase angle of 0 degrees means that the voltage and current waveforms are perfectly in phase. They rise and fall together, reaching their peaks and troughs at the same time.
Circuit Type for Zero Phase Angle: In an AC circuit, the voltage and current are in phase only when the circuit is purely resistive. In a purely resistive circuit, there are no reactive components (inductors or capacitors) to cause a phase shift between voltage and current.
Conclusion: Therefore, a power factor of 1 indicates that the circuit is purely resistive.
A) The circuit is purely resistive. As explained above, a power factor of 1 implies a phase angle of 0 degrees between voltage and current, which is characteristic of a purely resistive circuit.
B) The circuit has equal reactive and resistive components. If a circuit has both reactive and resistive components, the phase angle \(\phi\) will generally not be 0. If the reactive components (inductive and capacitive reactances) cancel each other out, then the circuit behaves like a purely resistive circuit, leading to a power factor of 1. However, simply having equal reactive and resistive components does not guarantee a power factor of 1. For example, if \(X_L = R\) and \(X_C = 0\), the power factor would be \(R/Z = R/\sqrt{R^2 + X_L^2} = R/\sqrt{R^2 + R^2} = R/\sqrt{2R^2} = 1/\sqrt{2} \approx 0.707\), not 1.
C) The voltage and current are out of phase. If the voltage and current are out of phase, the phase angle \(\phi\) is not 0. This would mean \(\cos(\phi) < 1\), so the power factor would be less than 1.
D) The circuit is purely inductive. In a purely inductive circuit, the current lags the voltage by 90 degrees (\(\phi = 90^\circ\)). The power factor would be \(\cos(90^\circ) = 0\), not 1.
To determine what happens to power when resistance increases at a constant voltage, we need to use the relevant formulas relating power, voltage, and resistance. Ohm's Law and the power formulas are key here.
Correct Option: B) Power decreases. As derived from the formula \(P = \frac{V^2}{R}\), with constant voltage, power is inversely proportional to resistance. Therefore, an increase in resistance leads to a decrease in power.
This question asks about different types of power in an AC circuit and which one does not contribute to useful work. Understanding the definitions of real, apparent, and reactive power is key to answering this question.
Correct Option: C) Reactive power is the type of power in an AC circuit that does not perform any useful work. It is required to build up and maintain the magnetic and electric fields in inductive and capacitive components, respectively, but it is not dissipated as heat or converted into mechanical energy.
The question asks about the type of electrical power that performs actual work in electrical devices. This requires understanding the different components of power in AC circuits and their physical significance.
Correct Option: A) Real power is the power that performs actual work in an electrical device. It is the component of power that is converted into useful forms of energy like mechanical work, heat, or light.
In DC circuits, which equation correctly describes the power?
The question asks for the correct equation describing power in DC circuits. We need to recall the fundamental definitions and relationships between power, voltage, and current, and then use Ohm's Law to derive alternative forms if necessary.
B) P = V * I
This is the fundamental definition of electrical power in a DC circuit, stating that power is the product of voltage and current. It is universally applicable to any DC component where voltage and current are known.