Transformer Equations

Potential Difference

The ratio of the voltage across the primary coil to the voltage across the secondary coil is equal to the ratio of the number of turns on the primary coil to the number of turns on the secondary coil.

This can be represented in the equation:

  • Vp = Potential difference (voltage) across the primary coil in volts (V)
  • Vs = Potential difference (voltage) across the secondary coil in volts (V)
  • np = Number of turns on the primary coil
  • ns = Number of turns on the secondary coil

Example

A transformer has 40 turns on its primary coil and 800 turns on its secondary coil. The input potential difference across the primary coil is 300 V. Calculate the potential difference obtained from the secondary coil.

Step 1: List the known quantities

  • Number of turns on the primary coil (np) = 40
  • Number of turns on the secondary coil (ns) = 800
  • Potential difference (voltage) across the primary coil (Vp) = 300 V

Step 2: Write down the equation

\dfrac{V_{p}}{V_{s}}=\dfrac{n_{p}}{n_{s}}\dfrac{V_{p}}{V_{s}}=\dfrac{n_{p}}{n_{s}}

Step 3: Rearrange the equation to find V_{s}V_{s}

V_{s}=V_{p}\times \dfrac{n_{p}}{n_{s}}V_{s}=V_{p}\times \dfrac{n_{p}}{n_{s}}

Step 4: Substitute the values into the equation

V_{s}=300\times \dfrac{800}{40}V_{s}=300\times \dfrac{800}{40}

So, the voltage from the secondary coil = 6,000 V

Transformer Efficiency and Power

To calculate electrical power, we use the equation:

  • P = Power in watts (W)
  • V = Potential difference in volts (V)
  • I = Current in amperes (A)

If a transformer is 100% efficient, then the input power is equal to the output power.

  • Vp × Ip = Input power (primary coil)
  • Vs × Is = Output power (secondary coil)

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