Root-Mean-Square Current & Voltage (CIE A Level Physics)

• 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:

• 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 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:

• Where:
  • I₀ = peak current (A)
  • V₀ = peak voltage (V)

• 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 any electrical component with resistance eg. a lamp

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

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

Step 2: Determine the peak voltage I₀

• • • • The alternating current equation is in the form: I = I₀ sin(⍵t)
      • Comparing this to I = 410 sin(100πt) means the peak current is I₀ = 410 A

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