Extended content
The effective value of sinusoidal alternating current is equal to the maximum value, so there is a special relationship between the effective value and the maximum value of sinusoidal alternating current. First, let's consider the waveform of sinusoidal alternating current.
Mathematically, sine function can be expressed as y=sin(x), where x is time and y is current value. At a certain moment t, the value of current can be expressed as I(t)=I_m*sin(wt+φ), where I_m is the maximum value, W is the angular velocity, and φ is the initial phase.
The effective value of sinusoidal alternating current is defined as the average value of current over a period of time, that is, I _ rms = (1/t) * ∫ (t1tot2) I (t) dt. Since the current is sinusoidal, we can use the integral formula of sine function to calculate this integral. We get I _ rms = (2/π) * I _ m by calculation.
This formula shows that the effective value of sinusoidal alternating current is equal to 2/π times the maximum value. This relationship is based on the calculation results of mathematical models, and it is also true in practical circuits.
In practical application, we usually use the effective value of sinusoidal alternating current to represent its magnitude, because the effective value can describe the influence of current on the circuit more accurately. For example, when we use a resistor in a circuit, the rated power of the resistor is designed according to the effective value of the current, not the maximum value. This is because the current that the resistor bears in actual operation is the effective value rather than the maximum value.
In short, there is a special relationship between the effective value and the maximum value of sinusoidal alternating current, that is, the effective value is equal to 2/π times of the maximum value. This relationship is very important in circuit design and analysis, because it can help us to understand and predict the influence of current on the circuit more accurately.