Question

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

Answer 1

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,

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

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.