Question

4. The amplitude of current in an RLC circuit with an alternating voltage source (AC), is given by $I = \frac{V_0}{\sqrt{R^2 + [\omega_a L - \frac{1}{\omega_a C}]^2}}$ where • R = resistance of the resistor (ohms, ?) • $V_0$ = amplitude of source voltage (volts, V) • L = inductance (henrys, H) • C = capacitance (farads, F) • $\omega_a = 2\pi f_a$ = angular frequency (rad/s, or more technically, 1/s) • $f_a$ = driving frequency (Hz, or 1/s) Because the voltage varies, the current also varies, and has a maximum value (amplitude) of I. This function computes that maximum value. Make a 3-D graph of I, as a function of $\omega_a$ and R, for 60 ? $f_a$ ? 110 Hz and 10 ? R ? 40 ? (ohms), and parameters $v_0$ = 24 V (volts), L = 0.30 H (henrys), and C = 12 x 10?? F (farads). Provide a title and label the axes with the relevant variables and brief descriptors of what the variables represent. Hint: Define a vector for $f_a$, then make the corresponding vector for $\omega_a$. You can then make the meshgrid with $\omega_a$, which is in the function formula and will be part of the graph (as opposed to $f_a$). Another hint: All of the single-valued parameters can (and should be) part of the computation for I, but pre-defined with variable names, so the values are not hardcoded in the formula.

          4. The amplitude of current in an RLC circuit with an alternating voltage source (AC), is
given by
$I = \frac{V_0}{\sqrt{R^2 + [\omega_a L - \frac{1}{\omega_a C}]^2}}$
where
• R = resistance of the resistor (ohms, ?)
• $V_0$ = amplitude of source voltage (volts, V)
• L = inductance (henrys, H)
• C = capacitance (farads, F)
• $\omega_a = 2\pi f_a$ = angular frequency (rad/s, or more technically, 1/s)
• $f_a$ = driving frequency (Hz, or 1/s)
Because the voltage varies, the current also varies, and has a maximum value (amplitude)
of I. This function computes that maximum value.
Make a 3-D graph of I, as a function of $\omega_a$ and R, for 60 ? $f_a$ ? 110 Hz and 10 ? R ?
40 ? (ohms), and parameters $v_0$ = 24 V (volts), L = 0.30 H (henrys), and C =
12 x 10?? F (farads).
Provide a title and label the axes with the relevant variables and brief descriptors of what
the variables represent.
Hint: Define a vector for $f_a$, then make the corresponding vector for $\omega_a$. You can then
make the meshgrid with $\omega_a$, which is in the function formula and will be part of the
graph (as opposed to $f_a$).
Another hint: All of the single-valued parameters can (and should be) part of the
computation for I, but pre-defined with variable names, so the values are not hardcoded
in the formula.

4. The amplitude of current in an RLC circuit with an alternating voltage source (AC), is
given by
I = (V0)/(√(R^2 + [ L - (1)/( C)]^2))
where
• R = resistance of the resistor (ohms, ?)
• V0 = amplitude of source voltage (volts, V)
• L = inductance (henrys, H)
• C = capacitance (farads, F)
• = 2π fa = angular frequency (rad/s, or more technically, 1/s)
• fa = driving frequency (Hz, or 1/s)
Because the voltage varies, the current also varies, and has a maximum value (amplitude)
of I. This function computes that maximum value.
Make a 3-D graph of I, as a function of and R, for 60 ? fa ? 110 Hz and 10 ? R ?
40 ? (ohms), and parameters v0 = 24 V (volts), L = 0.30 H (henrys), and C =
12 x 10?? F (farads).
Provide a title and label the axes with the relevant variables and brief descriptors of what
the variables represent.
Hint: Define a vector for fa, then make the corresponding vector for . You can then
make the meshgrid with , which is in the function formula and will be part of the
graph (as opposed to fa).
Another hint: All of the single-valued parameters can (and should be) part of the
computation for I, but pre-defined with variable names, so the values are not hardcoded
in the formula.

Added by Justin A.

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