Question

In: Physics

1. Describe "rms" in the context of an alternating current. Why do we use it? 2....

1.

Describe "rms" in the context of an alternating current. Why do we use it?

2. How is it possible to create a circuit in which adding more resistors and rearranging them actually decreases the Equivalent Resistance?

Please question 1 and 2 - thank you

Solutions

Expert Solution

1.The RMS(Root mean squared) value of Alternating current is the equivalent DC current that would
produce the same average power loss as the alternating current across a load. The RMS value is the square root of the mean (average) value of the squared function of the instantaneous values.

where im is the average current.

When dealing with AC, we face difficulty of what value of AC to use. One way is to use the Peak value of AC. Another method which is more common and practical is RMS value.

The RMS value of current gives the same heating effect as a Direct current of the same value would. That is if a direct current I passes through a resistance of R ohms, the DC power consumed by the resistor as heat will be I2R watts. Then if an alternating current, i = Imax*sinθ flows through the same resistance, the AC power converted into heat will be: I2rms*R watts.

RMS value of current gives us a standard to compare the amount of power that an AC and DC waveform can give to a circuit.

Most measuring devices like multimeters or voltmeters measure the RMS value of Alternating sinusoidal waveforms, and hence, RMS value is more practical the Average current.

2. Whenever we add two resistors in parallel, the equivalent resistance is given by

Assuming R1> >R2, Then,

(Neglecting R2 in comparison with R1 in denominator)

Thus,this equivalent resistance has a value equal to the lowest of two R1 and R2.

In Practical cases, when the difference of resistance is not large, this equivalent resistance has a value even lesser than lowest of two R1 and R2. Thus , Adding resistor in parallel always results in a decreased equivalent resistance.


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