# Alternating Currents

## Alternating Currents Revision

**Alternating Currents**

The **mains electricity supply** is** alternating current (A.C)**. This section looks at the features of A.C including **frequency**, **root-mean-square current** and **root-mean-square voltage**.

**Alternating Currents**

**Alternating current (A.C)** periodically varies from positive to negative **current**. If the alternating current supply is plotted against time, a **sinusoidal graph** is formed showing that the **electrons **in the wire move back and forth in **simple harmonic motion (SHM)**. The same concept could be used for plotting **voltage against time**.

The **time period** can be seen above on the graph and is the time difference between **two peak positive currents **or two peak negative currents. **Frequency **of the AC supply can also be calculated as:

f = \dfrac{1}{T}

- f is the
**frequency**in Hertz \left(\text{Hz}\right). - T is the
**time period**in seconds \left(\text{s}\right).

**Example:** The time period of an AC supply is 0.1 \: \text{s}. Calculate the frequency of the supply.

**[1 mark]**

f = \dfrac{1}{T}

f = \dfrac{1}{0.1}

f = 10 \: \text{Hz}

**Root-Mean-Square Current**

**Root-Mean-Square (rms)** is used to compare **AC** and **DC **(Direct Current) currents. The **rms** for direct current or voltage represents the value of direct current or voltage that will produce the same **power dissipation as alternating current**. The rms value is calculated by the square root of the mean of the squares of all values of voltage in one full cycle.

To calculate the **rms current** \left(I_{rms}\right), the following equation can be used:

I_{rms} = \dfrac{I_0}{\sqrt{2}}

where I_{rms} is the** rms current** and I_0 is the **peak current**. Both are measured in amps \left(\text{A}\right).

To calculate the **rms voltage** \left(V_{rms}\right), the following equation can be used:

V_{rms} = \dfrac{V_0}{\sqrt{2}}

where V_{rms} is the** rms voltage** and V_0 is the **peak voltage**. Both are measured in volts \left(\text{V}\right).

**Example:** The peak current read from an oscilloscope trace is 2.5 \: \text{A}. What is the rms current?

**[1 mark]**

I_{rms} = \dfrac{I_0}{\sqrt{2}}

I_{rms} = \dfrac{2.5}{\sqrt{2}}

I_{rms} = 1.8 \: \text{A}

**Applications of Alternating Current**

The **UK power supply** is an** alternating current/voltage**. It has a **peak voltage** of 230 \: \text{V} and the frequency of the alternating voltage is 50 \: \text{Hz} (switches from positive to negative 50 times per second). However, this is an average and varies depending upon the time of day, demand and type of consumer.

## Alternating Currents Example Questions

**Question 1:** What is meant by rms current?

**[2 marks]**

**The square root of the mean of the squares of all values of voltage in one full cycle.**

**Question 2: **The peak current read from an oscilloscope trace is 5.25 \: \text{A}. What is the rms current?

**[1 mark]**

**Question 3:** Give 2 factors that affect the peak voltage of the mains supply.

**[2 marks]**

Any two from:

**Time of day****Demand****Type of consumer**

## Alternating Currents Worksheet and Example Questions

### Alternating Current Questions

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