Question

A doorbell uses a transformer to deliver an amplitude of \(8.5 \mathrm{V}\) when it is connected to a \(170-\mathrm{V}\) amplitude line. If there are 50 turns on the secondary, (a) what is the turns ratio? (b) How many turns does the primary have?

Short answer

Answer: The turns ratio is approximately 20, and the primary coil has approximately 1000 turns.

Step-by-step solution

Identify the given information

We are given: - \(V_p = 170 \mathrm{V}\) (voltage of the primary coil) - \(V_s = 8.5 \mathrm{V}\) (voltage of the secondary coil) - \(N_s = 50\) (number of turns in the secondary coil)

Calculate the turns ratio

Using the formula for the turns ratio: $$\frac{N_p}{N_s}=\frac{V_p}{V_s}$$ Plug in the given values: $$\frac{N_p}{50}=\frac{170}{8.5}$$ Now, we can solve for the turns ratio, which is the ratio of \(N_p\) to \(N_s\): $$\frac{N_p}{50}=\frac{170}{8.5} \Rightarrow \frac{N_p}{50} \approx 20$$ So, the turns ratio is approximately 20.

Find the number of turns in the primary coil

Now that we have the turns ratio, we can find how many turns are in the primary coil. We know the following: $$\frac{N_p}{50} \approx 20$$ Now, we can solve for \(N_p\): $$N_p \approx 20 \times 50 = 1000$$ Therefore, the primary coil has approximately 1000 turns.