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The tuned circuit of FIGURE 3 has a Q-factor of 1000 and is

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The tuned circuit of FIGURE 3 has a Q-factor of 1000 and is designed to resonate at 1 MHz. At resonance the supply current, I, is measured as 15 μA for a supply voltage, Vs, of 2.5 V. The load resistor RL is 10 kΩ. (a) Calculate the bandwidth and half-power frequencies of the tuned circuit. (b) If C is set to 1 nF calculate the values of R and L. (c) Estimate the impedance offered to the supply at resonance and at the frequencies of ± 2% from resonance (use a ‘narrow-band’ approximation to find the impedance of the L-RC circuit).

If you wish, I can reply this question. I am asking you as you didn't upload figure in the other thread where I had shown intention to solve this problem.

FIGURE 5 shows an ideal autotransformer (k = 1 and no power losses). (a) Apply Kirchhoff’s laws to write down two equations to express the voltages V1 and V2 in terms of the self and mutual voltages induced across the two coils. (b) Hence obtain an expression for the voltage ratio V1 for the condition V2 L1 = 4L2. (c) Determine the supply voltage and current with a 10 Ω load carrying 100 A and L1 = 4L2.

Hi, in part (b) can you show me more detail/working out on how you got to jwL2(9I1-3I2) please. I folloe the I parts but how did you eliminate the rest. Thanks

For V1: i understand the inclusion of L1, K - mutual inductance, L2 but dont understand where the last part of the equation (jwMI1 - mutual inductance) comes from.

Also for V2: why is the RL not taken into account?