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

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 I_r.m.s is defined by the equation:

$I_{r.m.s}=\frac{I_0}{\sqrt{2}}$

• 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 V_r.m.s is defined by the equation:

$V_{r.m.s}=\frac{V_0}{\sqrt{2}}$

• 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

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