Question

The timing device in an automobile’s intermittent wiper system is based on RC antime constant and utilizes a$\mathbf{0}\mathbf{.}\mathbf{500}\mathbf{-}\mathbf{\mu F}$capacitor and a variable resistor. Over what range must be made to vary to achieve time constants from$\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{to}\mathbf{}\mathbf{15}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{s}$?

Short answer

To achieve the time constants the range of R must be$R=4M\Omega -30M\Omega$

Step-by-step solution

Concept Introduction

The rate of electron flow can be described as the aggregate flow of electrons via a wire. The term "resistance" refers to anything that stands in the way of current flow. To convert electrical energy to light, heat, or movement, an electrical circuit must have resistance.

Information Provided

The timing device in an automobile's intermittent wiper system is based on an RC time constant and utilizes a $0.500\mathrm{\mu F}$capacitor and a variable resistor.

The values are $\tau =2.00sandC=0.500\mu F\left(\frac{{10}^{-6}F}{1\mu F}\right)=5.00\times {10}^{-7}F$

Minimum Range for resistance

The time constant for the RC circuit is given as,

$\tau =RC$……………….(1)

Where$\tau$is the time constant, R is the resistance of the circuit, and C is the capacitance of the circuit.

The minimum resistance is given by substituting$\tau =2.00s$and $C=5.00\times {10}^{-7}F$in equation (1), such that

$$\begin{gathered} 2.00s=R\times \left(5.00\times {10}^{-7}F\right) \\ R=\frac{22.00s}{5.00\times {10}^{-7}F} \\ R=4.0\times {10}^6\Omega \left(\frac{1M\Omega }{{10}^6\Omega }\right) \\ R=4.0M\Omega \end{gathered}$$

Maximum Range for resistance

The maximum resistance is given by substituting $\tau =15.0s$and $C=5.00\times {10}^{-7}F$in equation (1), such that

$$\begin{gathered} 15.0s=R\times \left(5.00\times {10}^{-7}F\right) \\ R=\frac{15.0s}{5.000\times {10}^{-7}F} \\ R=30.0\times {10}^6\Omega \left(\frac{1M\Omega }{{10}^6\Omega }\right) \\ R=30.0M\Omega \end{gathered}$$

Therefore, the range is role="math" localid="1656398436584" $4.0M\Omega to30.0M\Omega$