Chapter 1, Problem 1.1P

Given an electrical quantity described in terms of words, scientific notation, or decimal prefix notation, convert the quantity to an alternate description. See Exercise 1-1.

1-1 Express the following quantities to the nearest standard prefix using no more than three digits.

1. 20,000 Hz
2. 1025 W
3. $0.333\times {10}^{-8}\text{s}$
4. $33\times {10}^{-12}\text{F}$

To determine

To express: The given quantity in nearest standard prefix notation.

Answer to Problem 1.1P

Using standard prefix notation, the quantity becomes $20\text{ MHz}$ .

Explanation of Solution

Given:

The quantity is $20,000,000\text{ Hz}$ .

Calculation:

According to the standard prefix notation, mega (M) is used to denote ${10}^6$ .

So, the given quantity can be expressed as

  $20,000,000\text{ Hz}=20\times {10}^6\text{ Hz}=20\text{ MHz}$ .

Conclusion:

Therefore, using standard prefix notation, the quantity becomes $20\text{ MHz}$ .

To determine

To express: The given quantity in nearest standard prefix notation.

Answer to Problem 1.1P

Using standard prefix notation, the quantity becomes $1.02\text{ kW}$ .

Explanation of Solution

Given:

The quantity is $1025\text{ W}$ .

Calculation:

According to the standard prefix notation, kilo (k) is used to denote ${10}^3$ .

So, the given quantity can be expressed as

  $1025\text{ W}=1.025\times {10}^3\text{ W}=1.025\text{ kW}$ .

Since maximum three digits can be used, the nearest equivalent expression using standard prefix notation will be

  $1025\text{ W}=1.02\text{ kW}$

Conclusion:

Therefore, using standard prefix notation, the quantity becomes $1.02\text{ kW}$ .

To determine

To express: The given quantity in nearest standard prefix notation.

Answer to Problem 1.1P

Using standard prefix notation, the quantity becomes $3.33\text{ ns}$ .

Explanation of Solution

Given:

The quantity is $0.333\times {10}^{-8}\text{ s}$ .

Calculation:

According to the standard prefix notation, nano (n) is used to denote ${10}^{-9}$ .

So, the given quantity can be expressed as

  $0.333\times {10}^{-8}\text{ s}=3.33\times {10}^{-9}\text{ s}=3.33\text{ ns}$ .

Conclusion:

Therefore, using standard prefix notation, the quantity becomes $3.33\text{ ns}$ .

To determine

To express: The given quantity in nearest standard prefix notation.

Answer to Problem 1.1P

Using standard prefix notation, the quantity becomes $33\text{ pF}$ .

Explanation of Solution

Given:

The quantity is $33\times {10}^{-12}\text{ F}$ .

Calculation:

According to the standard prefix notation, pico (p) is used to denote ${10}^{-12}$ .

So, the given quantity can be expressed as

  $33\times {10}^{-12}\text{ F}=33\text{ pF}$ .

Conclusion:

Therefore, using standard prefix notation, the quantity becomes $33\text{ pF}$ .