RLC Circuits and Electrical Systems Quiz

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Which energy storage element stores energy in the capacitor in the given circuit?

Capacitor (correct)

Resistor

Inductor

Voltage source

What is the first state equation for the given circuit?

$\frac{di}{dt} = \frac{1}{R}(v_s - v_1 - L_i)$

$\frac{dv_1}{dt} = \frac{1}{L}i$

$\frac{di}{dt} = \frac{1}{L}(v_s - v_1 - R_i)$ (correct)

$\frac{dv_1}{dt} = \frac{1}{C}i$

What concept allows us to deal with algebraic equations rather than differential equations in circuit analysis?

Laplace transform (correct)

Impedance

State variables

Transfer function

According to the text, what is the equation for planar motion when an object can translate in two dimensions and rotate only about an axis perpendicular to the plane?

$I_O \omegȧ = M_O$ Signup and view all the answers

What is the mass moment of inertia defined as?

$I = r^2 dm$ Signup and view all the answers

What is the formula for the mass moment of inertia about a rotation axis parallel to the body's axis of symmetry at a distance d?

$I = Is + md^2$ Signup and view all the answers

Which equation represents the relationship between the velocities of mass mA and mass mB in the given system?

ẋ + 3ẏ = 0 Signup and view all the answers

What is the acceleration of block B in the pulley system when using free body diagrams?

2g/11 Signup and view all the answers

What is the total energy in the system in the given pulley system problem?

mAẋA + mBẋB - mAgxA - mBgxB Signup and view all the answers

What is the relationship between the velocities ẋA and ẋB in the given pulley system problem?

ẋA = -ẋB/2 Signup and view all the answers

According to the parallel-axis theorem, what is the moment of inertia of a sphere of mass m and radius R about an axis parallel to and a distance d away from its center?

$I = mR^2 + md^2$ Signup and view all the answers

In the single-drum hoist problem, what is the equation of motion for the drum?

$mL^2θ̈ = -mgLsinθ$ Signup and view all the answers

In the pendulum with a concentrated mass problem, what is the linearized equation of motion assuming small angles?

$Lθ̈ = -gθ$ Signup and view all the answers

What is the work-energy relationship for rotational motion?

$KE = Iω^2/2$ Signup and view all the answers

According to the text, which condition satisfies the approximation that the tension forces in the cable are approximately equal?

The pulley inertia is negligible compared to other inertias in the system Signup and view all the answers

In the pulley system shown in Figure 3.2.6a, if the pulley inertia is nonnegligible, how does it affect the result of m1 lifting m2?

The pulley inertia decreases the speed with which m1 lifts m2 Signup and view all the answers

What is the equation of motion for the pulley system shown in Figure 3.2.6a, in terms of x?

$ẍ = (m1 - m2)g - (m1 + m2)ẍ$ Signup and view all the answers

What is the expression for the tension force T1 in the cable of the pulley system shown in Figure 3.2.6a?

$T1 = m1g - m1ẍ$ Signup and view all the answers