Question #297024

1.The equivalent resistance of two resistors Ri and Rz connected in parallel is given Rey = If R, = 100.0 +5% and R = 47.0 + 5%, find the expected maximum and minimum value of their equivalent resistance when they are connected in parallel.



2. A particle moves in a straight line such that its displacement, x meters, from a fixed point on the line at time t seconds is given by x = 40[e-2t - e-4]. (a) Find the time when the particle is instantaneously at rest. (b) Find the displacement of the particle from O when t = 3 s. (c) Find the total distance travelled during the first 3 seconds of its

1
Expert's answer
2022-02-13T12:15:46-0500

Explanations & Calculations


a)

  • In a parallel combination, the equivalent resistance always results lower than even the lowest resistance in the combination.
  • Therefore, if we are to calculate the lowest resistance, it should be when the 2 resistances are at their minimum values and vice versa.
  • Then proceeding with this yields,

R1max=100+5%=105ΩR1min=1005%=95ΩR2max=47.0+5%=49.4ΩR2min=47.05%=44.7ΩReq=R1.R2R1+R2Reqmin=95.0×44.795.0+44.7=30.4ΩReqmax=105×49.4100+49.4=33.6Ω\qquad\qquad \begin{aligned} \small R_{1-max}&=\small 100+5\%=105\,\Omega\\ \small R_{1-min} &= \small 100-5\%=95\,\Omega\\ \\ \small R_{2-max}&=\small 47.0+5\%=49.4\,\Omega\\ \small R_{2-min}&=\small 47.0-5\%=44.7\,\Omega\\ \\ &\therefore\\ \\ \small R_{eq}&=\small \frac{R_1.R_2}{R_1+R_2}\\ \\ \small R_{eq-min}&=\small \frac{95.0\times44.7}{95.0+44.7}=30.4\,\Omega\\ \\ \small R_{eq-max}&=\small \frac{105\times49.4}{100+49.4}=33.6\,\Omega \end{aligned}


b)

  • Differentiating the distance function once with respect to time gives the formula of instantaneous velocity as a function of time.
  • Equaling that formula to zero representing the zero velocity, you can solve for the time.


  • Just by substituting the time of t=3 into the distance equation, you can have the distance of the object from O at that time.


  • The distance function alone represents the instantaneous distance the object record with time.
  • Therefore, integrating the distance function with respect to time gives you the summation of the ins. distances until t = 3s which gives you the total distance travelled during that period of time.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS