Question
A resistor of resistance \(R\) is connected to an alternating current power supply. The peak voltage across the resistor is \(V_0\). What is the mean power dissipated by the resistor?
A. \(\frac{V_0^2 \sqrt{2}}{R}\)
B. \(\frac{V_0^2}{R}\)
C. \(\frac{V_0^2}{R \sqrt{2}}\)
D. \(\frac{V_0^2}{2 R}\)
▶️Answer/Explanation
Ans:D
The mean power \((P)\) dissipated by a resistor in an alternating current (AC) circuit can be calculated using the root mean square (RMS) values of current and voltage. In this case, the peak voltage \(\left(V_0\right)\) is given. The RMS voltage \(\left(V_{\text {rms }}\right)\) for a sinusoidal AC waveform is related to the peak voltage as follows:
\[
V_{\mathrm{rms}}=\frac{V_0}{\sqrt{2}}
\]
The mean power dissipated by the resistor is given by:
\[
P=I_{\mathrm{rms}}^2 \cdot R
\]
In an \(\mathrm{AC}\) circuit with a purely resistive component, the RMS current is related to the RMS voltage and resistance as follows:
\[
I_{\mathrm{rms}}=\frac{V_{\mathrm{rms}}}{R}=\frac{V_0}{R \sqrt{2}}
\]
Now, we can calculate the mean power:
\[
P=\left(\frac{V_0}{R \sqrt{2}}\right)^2 \cdot R=\frac{V_0^2}{2 R}
\]
Question
Three changes are made to a transformer.
I. increasing the thickness of wire in the coils
II. laminating the soft iron core
III. using wire with lower resistivity
Which changes will reduce power losses in the transformer?
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
▶️Answer/Explanation
Ans:D
Reducing power losses in a transformer involves minimizing both copper losses and iron losses. Let’s evaluate each change and its impact on power losses:
I. Increasing the thickness of wire in the coils:
- Increasing the thickness of wire reduces the resistance of the coil, which decreases copper losses (I²R losses). So, this change reduces copper losses and is beneficial for reducing power losses.
II. Laminating the soft iron core:
- Laminating the core reduces eddy current losses, which are a type of iron loss in transformers. By minimizing eddy currents, this change reduces iron losses, making it beneficial for reducing power losses.
III. Using wire with lower resistivity:
- Using wire with lower resistivity further decreases the resistance of the coil, reducing copper losses (I²R losses). This change is also beneficial for reducing power losses.
So, all three changes will reduce power losses in the transformer. Therefore, the correct answer is:D
Question
Wire XY moves perpendicular to a magnetic field in the direction shown.
The graph shows the variation with time of the displacement of XY.
What is the graph of the electromotive force \((\mathrm{emf}) \varepsilon\) induced across \(\mathrm{XY}\) ?
▶️Answer/Explanation
Ans:C
Induced Voltage (emf)
An emf is induced in a conductor moving in a magnetic field. A conducting wire of length \(L\) moves perpendicularly to a uniform magnetic field \(\boldsymbol{B}\) with constant velocity \(\boldsymbol{v}\).
Force on electrons in the wire:
\[
\vec{F}=q \vec{v} \times \vec{B}
\]
Since force \(\boldsymbol{F}\) on electrons is upward, \(I\) is downward in the wire.
\[
V=B v L \text { (Potential difference) }
\]
An emf is induced and a current flows in the wire as long as it moves in the magnetic field. (principle of the electric generator).
So, from this Emf is directly proportional to v(velocity).
So, from $0$ to $t_1$ velocity will increase , and it become constant up to $t_2$ and will start decreasing .
So, graph will like option -C
Question
Which law is equivalent to the law of conservation of energy?
A. Coulomb’s law
B. Ohm’s Law
C. Newton’s first law
D. Lenz’s law
▶️Answer/Explanation
Ans:D
Lenz’s law is indeed based on the principle of the conservation of energy. It states that the direction of an induced electromotive force (emf) and the induced current in a closed circuit will always be such that they oppose the change in magnetic flux that produced them. This is in accordance with the law of conservation of energy because it implies that work is done to overcome the opposition, and this work results in the transformation of energy.
When an external force is applied to move a conductor through a changing magnetic field (or vice versa), work is done, and this work is ultimately converted into electrical energy in the form of induced current. The law of conservation of energy dictates that the total energy in the system remains constant. Therefore, the extra effort to overcome the opposition and induce the current is indeed transformed into electrical energy, thus conserving energy in the process.
Question
An ac generator produces a root mean square \((\mathrm{rms})\) voltage \(V\). What is the peak output voltage when the frequency is doubled?
A. \(\frac{2}{\sqrt{2}} V\)
B. \(\frac{V}{2 \sqrt{2}}\)
C. \(\frac{\sqrt{2}}{2} V\)
D. \(2 \sqrt{2} \mathrm{~V}\)
▶️Answer/Explanation
Ans:D