The circuit given in the figure is driven by a voltage source $V_s = 25\sqrt{2}\angle 30^\circ V$. The system is operating at a frequency of 50 Hz. The transformers are assumed to be ideal. The average power dissipated, in W, in the $50 k\Omega$ resistance is ________ (rounded off to two decimal places).
The circuit given in the figure is driven by a voltage source $V_s = 25\sqrt{2}\angle 30^\circ V$. The system is operating at a frequency of 50 Hz. The transformers are assumed to be ideal. The average power dissipated, in W, in the $50 k\Omega$ resistance is ________ (rounded off to two decimal places).
Show Hint
Correct Answer: 31
Solution and Explanation
Step 1: Reflect the $50 k\Omega$ resistor through the second transformer.
The impedance seen at the primary of the second transformer is $Z_{p2} = \frac{50 \times 10^3}{10^2} = 500 \Omega$.
Step 2: Calculate the total impedance on the secondary side of the first transformer.
$Z_{s1} = 400 \Omega + Z_{p2} = 400 \Omega + 500 \Omega = 900 \Omega$.
Step 3: Reflect this impedance through the first transformer to the primary side.
The impedance seen by the source (excluding the $1 \Omega$ resistor) is $Z_{p1} = \frac{Z_{s1}}{10^2} = \frac{900}{100} = 9 \Omega$.
Step 4: Calculate the total impedance seen by the voltage source.
$Z_{total} = 1 \Omega + Z_{p1} = 1 \Omega + 9 \Omega = 10 \Omega$.
Step 5: Calculate the current drawn from the voltage source.
$I_1 = \frac{V_s}{Z_{total}} = \frac{25\sqrt{2}\angle 30^\circ}{10} = 2.5\sqrt{2}\angle 30^\circ A$.
Step 6: Calculate the current in the secondary of the first transformer.
$I_2 = \frac{I_1}{10} = \frac{2.5\sqrt{2}\angle 30^\circ}{10} = 0.25\sqrt{2}\angle 30^\circ A$.
Step 7: Calculate the current in the secondary of the second transformer (through the $50 k\Omega$ resistor).
$I_4 = \frac{I_2}{10} = \frac{0.25\sqrt{2}\angle 30^\circ}{10} = 0.025\sqrt{2}\angle 30^\circ A$.
Step 8: Calculate the average power dissipated in the $50 k\Omega$ resistor. $P = |I_{4,rms}|^2 R = \left(\frac{|I_4|}{\sqrt{2}}\right)^2 R = \left(\frac{0.025\sqrt{2}}{\sqrt{2}}\right)^2 \times 50 \times 10^3 = (0.025)^2 \times 50000 = 0.000625 \times 50000 = 31.25 W$.
Top GATE IN Electrical Circuits Questions
The circuit shown in Figure (a) can be represented using its equivalent T-model as shown in Figure (b). The values of the inductances $L_1$, $L_2$, and $L_3$ in the equivalent T-model are
- Three parallel admittances \( Y_a = 0.2j \, {S}, \, Y_b = -0.3j \, {S}, \, Y_c = 0.4 \, {S} \) are connected in parallel with a voltage source \( V_s = 10\angle 45^\circ \, {V} \), drawing a total current \( I_s \) from the source. The currents flowing through each of these admittances are \( I_a, I_b, I_c \), respectively. Let \( I = I_b + I_c \). The phase relation between \( I \) and \( I_s \) is:
- The circuits mentioned in the following options are realized using ideal opamp. Among these, the circuit(s) performing non-linear operation on the input signal is/are:
The clock frequency of the digital circuit shown in the figure is 12 MHz. The frequencies of the output (F) corresponding to Control = 0 and Control = 1, respectively, are
The bridge circuit, shown in Figure (a), can be equivalently represented using the circuit shown in Figure (b). The values of $R_1$, $R_2$, and $V_C$ in the equivalent circuit are
Top GATE IN Electrical Circuits Questions
The circuit shown in Figure (a) can be represented using its equivalent T-model as shown in Figure (b). The values of the inductances $L_1$, $L_2$, and $L_3$ in the equivalent T-model are
- Three parallel admittances \( Y_a = 0.2j \, {S}, \, Y_b = -0.3j \, {S}, \, Y_c = 0.4 \, {S} \) are connected in parallel with a voltage source \( V_s = 10\angle 45^\circ \, {V} \), drawing a total current \( I_s \) from the source. The currents flowing through each of these admittances are \( I_a, I_b, I_c \), respectively. Let \( I = I_b + I_c \). The phase relation between \( I \) and \( I_s \) is:
- The circuits mentioned in the following options are realized using ideal opamp. Among these, the circuit(s) performing non-linear operation on the input signal is/are:
The clock frequency of the digital circuit shown in the figure is 12 MHz. The frequencies of the output (F) corresponding to Control = 0 and Control = 1, respectively, are
The bridge circuit, shown in Figure (a), can be equivalently represented using the circuit shown in Figure (b). The values of $R_1$, $R_2$, and $V_C$ in the equivalent circuit are
Top GATE IN Questions
Despite his initial hesitation, Rehman’s ____________ to contribute to the success of the project never wavered.
Select the most appropriate option to complete the above sentence.Bird : Nest :: Bee : __________
Select the correct option to complete the analogy.- If \( P e^x = Q e^{-x} \) for all real values of \( x \), which one of the following statements is true?
The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube? Note: The figures shown are representative.
- Let \( p_1 \) and \( p_2 \) denote two arbitrary prime numbers. Which one of the following statements is correct for all values of \( p_1 \) and \( p_2 \)?