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:
- 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 Vr.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
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 = 410 sin(100πt)
where I is measured in amperes and t is in seconds.For this alternating current, determine the r.m.s current.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 Ir.m.s equation
