Answer to Question #297024 in Electric Circuits for mosaddek

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,

"\\qquad\\qquad\n\\begin{aligned}\n\\small R_{1-max}&=\\small 100+5\\%=105\\,\\Omega\\\\\n\\small R_{1-min} &= \\small 100-5\\%=95\\,\\Omega\\\\\n\\\\\n\\small R_{2-max}&=\\small 47.0+5\\%=49.4\\,\\Omega\\\\\n\\small R_{2-min}&=\\small 47.0-5\\%=44.7\\,\\Omega\\\\\n\\\\\n&\\therefore\\\\\n\\\\\n\\small R_{eq}&=\\small \\frac{R_1.R_2}{R_1+R_2}\\\\\n\\\\\n\\small R_{eq-min}&=\\small \\frac{95.0\\times44.7}{95.0+44.7}=30.4\\,\\Omega\\\\\n\\\\\n\\small R_{eq-max}&=\\small \\frac{105\\times49.4}{100+49.4}=33.6\\,\\Omega\n\\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.

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