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IB DP Physics: HL復(fù)習(xí)筆記11.2.2 Root-Mean-Square Current & Voltage

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年8月2日上午11:41

Root-Mean-Square Current & Voltage

Direct current sources provide a constant voltage and current over time, making it easy to measure
In situations involving alternating voltage and current, the average values of voltage and current will?always be zero
- This can make it difficult to measure

11-1-2-alternating-current-and-voltage-mean-value-ib-hl

The mean value for alternating current and voltage is always zero

The use of?root mean square?values gets around this problem
- First remove all the negative signs by simply squaring the peak current, or voltage
- Find the average of the squared value
- And finally, take the square root

Root-mean-square (rms) values of current, or voltage, are a useful way of?comparing?a.c current, or voltage, to its equivalent direct current (d.c), or voltage
- The rms values represent the direct current, or voltage, values that will produce the same?heating effect, or power dissipation, as the alternating current, or voltage

The rms value of an alternating current is defined as:

The square root of the mean of squares of all the values of the current in one cycle

An alternate definition is:

The equivalent direct current that produces the same power

A resistive load is any electrical component with resistance eg. a lamp

21.1-RMS-v-Peak-graph

Vrms?and peak voltage. The rms voltage is about 70% of the peak voltage

Worked Example

An electric oven is connected to a 230 V root mean square (rms) mains supply using a cable of negligible resistance.

Calculate the peak-to-peak voltage of the mains supply.

Step 1: Write down the Vrms equation

Exam Tip

Remember to double-check the units on the alternating current and voltage graphs. These are often shown in milliseconds (ms) instead of seconds (s) on the x-axis.