A LevelPhysicsCambridge (CIE)Revision Notes21. Alternating CurrentsCharacteristics of Alternating CurrentsRoot-Mean-Square Current & Voltage

Root-Mean-Square Current & Voltage (Cambridge (CIE) A Level Physics): Revision Note

Exam code: 9702

Katie M

Author

Katie M

Last updated

Root-mean-square current & voltage

  • Root-mean-square (r.m.s) values of current, or voltage, are a useful way of comparing a.c current, or voltage, to its equivalent direct current, or voltage

  • The r.m.s values represent the d.c current, or voltage, values that will produce the same heating effect, or power dissipation, as the alternating current, or voltage

  • The r.m.s value of an alternating current is defined as:

    The value of a constant current that produces the same power in a resistor as the alternating current

  • The r.m.s current Ir.m.s is defined by the equation:

I subscript r. m. s end subscript space equals space fraction numerator space I subscript 0 over denominator square root of 2 end fraction

  • The r.m.s value of an alternating voltage is defined as:

    The value of a constant voltage that produces the same power in a resistor as the alternating voltage

  • The r.m.s voltage Vr.m.s is defined by the equation:

V subscript r. m. s end subscript space equals space fraction numerator space V subscript 0 over denominator square root of 2 end fraction

  • Where:

    • I0 = peak current (A)

    • V0 = peak voltage (V)

  • So, r.m.s current is equal to 0.707 × I0, which is about 70% of the peak current I0

  • The r.m.s value is therefore defined as:

    The steady direct current, or voltage that delivers the same average power in a resistor as the alternating current, or voltage

  •  A resistive load is an electrical component with resistance e.g. a lamp

Peak voltage and RMS voltage

RMS v Peak grap, downloadable AS & A Level Physics revision notes

Vr.m.s and peak voltage. The r.m.s voltage is about 70% of the peak voltage

Worked Example

An alternating current is I is represented by the equation

I space equals space 410 space sin open parentheses 100 straight pi t close parentheses

where I is measured in amps and t is in seconds.

For this alternating current, determine

(a) the r.m.s current

(b) the frequency. 

Answer:

(a)

Step 1: Write out the equation for r.m.s current

I subscript r. m. s end subscript space equals space fraction numerator I subscript 0 space over denominator square root of 2 end fraction

Step 2: Determine the peak voltage I0

  • The alternating current equation is in the form: I space equals space I subscript 0 sin open parentheses omega t close parentheses

  • Comparing this to I space equals space bold 410 sin open parentheses 100 straight pi t close parenthesesmeans the peak current is I0 = 410 A

Step 3: Substitute into the Ir.m.s equation

I subscript r. m. s end subscript space equals space fraction numerator 410 over denominator square root of 2 end fraction space equals space 290 space straight A

(b)

Step 1: Write out the equation for angular frequency

omega space equals space 2 straight pi f

Step 2: Determine the angular frequency

  • The alternating current equation is in the form: I space equals space I subscript 0 sin open parentheses omega t close parentheses

  • Comparing this to I space equals space 410 sin open parentheses bold 100 bold pi t close parenthesesmeans the angular frequency is ω = 100π rad s−1

Step 3: Rearrange and substitute into the equation to calculate frequency

f space equals space fraction numerator omega over denominator 2 straight pi end fraction space equals space fraction numerator 100 straight pi over denominator 2 straight pi end fraction space equals space 50 space Hz

Examiner Tips and Tricks

These equations are not given on your data sheet, so make sure you learn them!

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Test yourself
    Previous:Alternating Current & VoltageNext:Mean Power
    Katie M

    Author: Katie M

    Expertise: Physics Content Creator

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.