Calculating potential differences
The ratio of potential differences on the transformerAn electrical device that increases, or decreases, the potential difference (voltage) of an alternating current. coils matches the ratio of the numbers of turns on the coils.
This equation can be used to calculate what the output might be from a particular transformer, or to work out how to design a transformer to make a particular potential difference change:
\(\frac{potential~difference~across~primary~coil}{potential~difference~across~secondary~coil} = \)
\(\frac{number~of~turns~in~primary~coil}{number~of~turns~in~secondary~coil}\)
This is when:
- the potential difference in the primary (input) coil is in volts (V)
- the potential difference in the secondary (output) coil is in volts (V)
In a step-up transformer, the potential difference in the secondary coil is greater than the potential difference in the primary coil. In a step-down transformer, the potential difference in the secondary coil is less than the potential difference in the primary coil.
Example
A mains transformer (230 V) has 11,500 turns on its primary coil and 600 turns on its secondary coil. Calculate the potential difference obtained from the secondary coil.
\(\frac{potential~difference~across~primary}{potential~difference~across secondary~coil} = \)
\( \frac{number~of~turns~in~primary}{number~of~turns~in~secondary~coil }\)
First rearrange the formula:
\(potential~difference~across~secondary~coil =\)
\(potential~ difference~across~primary~coil \times \)
\( \frac{number~of~turns~in~secondary~coil}{number~of~turns~in~primary~coil }\)
\(potential~difference~across~secondary~coil = 230 \times \frac{600}{11,500}\)
\(potential~difference~from~secondary~coil = 12~V~(to~2~sf)\)
The transformer in the example above is a step-down transformer. This is because there are fewer turns on the secondary coil, and there is a smaller potential difference on the secondary coil.
This type of transformer would typically be used to operate or charge household equipment that could also be battery operated, such as radios, doorbells and laptops.
Power in transformers
If the transformer is 100% efficient, the power in each coil will be the same - this means that:
potential difference across primary coil 脳 current in primary coil = potential difference across secondary coil 脳 current in secondary coil
\(V_{P} \times I_{P} = V_{S} \times I_{S}\)
Electricity is generated in a power station at 25,000 V, and to transmit the electricity across the country on the National GridThe network that connects all of the power stations in the country to make sure that everywhere has access to electricity., transformers increase the potential difference to 400,000 V.
This means that the transformer increases the potential difference by a factor of 16. So if there are no energy losses in the system, the current would also be reduced by a factor of 16 as:
power = potential difference 脳 current
Reducing the current by a factor of 16 means that the heating effect of the current is reduced by a factor of 256 (162), as:
power = current2 脳 resistance
This means that the energy is transferred more efficiently, as less energy is dissipated as heat.
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