Question

Verify that after a time of \(10.0{\rm{ }}ms\), the current for the situation considered in Example \(23.9\) will be \(0.183{\rm{ }}A\) as stated.

Short answer

The current\(0.183\)will be\(0.183A\)as stated.

Step-by-step solution

Concept Introduction

Current is the movement of electrical charge carriers, often electrons or atoms deficient in electrons.\(I\)in capital letters is a common symbol for "current." The standard unit is the ampere, denoted by the letter\(A\).

Information Provided

• The current value is:\(0.183A\)
• The time value: \(10.0{\rm{ }}ms\)

Calculating the Current

What we know is that at the end of each period\(\tau \), the current is\(0.368\)times the current at the start of the period. Four of these periods have elapsed in our circumstance. As a result, the current will be

\(\begin{array}{c}I = {I_0} \times {0.368^4}\\ = 0.0183{I_0}\end{array}\)

If we substitute the value of the initial current,\({I_0} = 10\;A\), we get our result,\(I = 0.183\;A\)

\(\begin{array}{c}{0.368^4} \times 10\\ = 0.183\end{array}\)

Therefore, the required solution is \(0.183\).