The quadratic mean (or root mean square) is usually used in physical applications. In power distribution systems, for example, voltages and currents are usually referred to in terms of their root mean square value. The quadratic mean of a set of values is obtained by squaring each value, adding the results, dividing by the number of values (n), and then taking the square root of that
Result, expressed as
$$\text { quadratic mean } = \sqrt { \frac { \sum x ^ { 2 } } { n } }$$ Find the root mean square of these power supplies (in volts): 56, 53, 22, 20.
A) 20.7 volts
B) 37.8 volts
C) 41.3 volts
D) 75.5 volts

Question

The quadratic mean (or root mean square) is usually used in physical applications. In power distribution systems, for example, voltages and currents are usually referred to in terms of their root mean square value. The quadratic mean of a set of values is obtained by squaring each value, adding the results, dividing by the number of values (n), and then taking the square root of that
Result, expressed as
 $$\text { quadratic mean } = \sqrt { \frac { \sum x ^ { 2 } } { n } }$$ Find the root mean square of these power supplies (in volts): 56, 53, 22, 20.
A) 20.7 volts
B) 37.8 volts
C) 41.3 volts
D) 75.5 volts

Quizplus · Accepted Answer

To find the root mean square, square each value: 56^2 = 3136, 53^2 = 2809, 22^2 = 484, 20^2 = 400. Sum these squares: 3136 + 2809 + 484 + 400 = 6829. Divide by the number of values (4): 6829 / 4 = 1707.25. Take the square root: √1707.25 ≈ 41.3 volts.

The Quadratic Mean (Or Root Mean Square) Is Usually Used quadratic mean =∑x2n\text { quadratic mean } = \sqrt { \frac { \sum x ^ { 2 } } { n } } quadratic mean =n∑x2​​

The Quadratic Mean (Or Root Mean Square) Is Usually Used $\text { quadratic mean } = \sqrt { \frac { \sum x ^ { 2 } } { n } }$