a sinusoidal voltage v 425 sin100t where v is in volts and t is in seconds is applied to a serie

Step 1: Calculate the impedance of the circuit using the formula Z = sqrt(R^2 + (X_L - X_C)^2),

A sinusoidal voltage v 425 sin100t where v is in volts and t...

A sinusoidal voltage Δv = 42.5 sin(100t), where Δv is in volts and t is in seconds, is applied to a series RLC circuit with L = 170 mH, C = 99.0 µF, and R = 65.0 Ω. (a) What is the impedance (in Ω) of the circuit? Ω (b) What is the maximum current (in A)? A (c) Determine the numerical value for ω (in rad/s) in the equation i = Imax sin(ωt − ϕ). rad/s (d) Determine the numerical value for ϕ (in rad) in the equation i = Imax sin(ωt − ϕ). rad (e) What If? For what value of the inductance (in H) in the circuit would the current lag the voltage by the same angle ϕ as that found in part (d)? H (f) What would be the maximum current (in A) in the circuit in this case?

Transcript

00:01 High students in this question, a series lcr circuit is being given with the value of inductance l to be equal to 170 into 10 raised to minus 3 henry, while the value of capacitance c will be equal to 99 into 10 raised to minus 6 ferret and finally the value of persistence r will be equal to 65 o.

00:20 Now the voltage of this circuit is given as delta v to be equal to 42 .5 into sine value of 100, from which we get the value of angular frequency omega to be equal to 100 radiance per second.

00:37 Now in the first part of the question, we are asked to find out the value of impedance z, which can be found out using the equation.

00:44 Imbedence z to be equal to square root the value of r square plus xl minus xc the whole square, where this xl corresponds to inductive reactants and xc corresponds to capacitive reactants.

01:00 Now the value of xl will be equal to l into omega.

01:04 On the other hand, the value of xc will be equal to 1 divided by c into omega.

01:09 Now by substituting the values, we get the value of xl to be equal to 17 om.

01:15 On the other hand, the value of xc will be equal to 101 .1 .1 .m.

01:23 Now by substituting all the values in the equation of z, we get z to be equal to square root the value of 6.

01:30 65 square plus 17 minus 101 .10 .0 .1 .1, the whole square, which on simplification gives the value of the impedance to be equal to 106 .2.

01:44 Now in the second part of the question, we are asked to find out the value of maximum current i max.

01:50 And the equation of this maximum current is taken as i max to be equal to the voltage maximum or the v max divided by impedance.

02:00 And in this question the value of v max is taken to be a value of 42 .5 volt.

02:08 Now by substituting the value of v max and z in the equation of i max we get the final answer of i max to be equal to a value of 0 .4 ambler.

02:19 Now in the third part of the question we are asked to find out the value of omega whenever the current i is taken to be i max into a sign value of omega t minus 5.

02:33 Now it should be noted that for a particular lcr circuit, its omega value will always remains to be a constant value...

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