A step-down transformer has 200 turns of wire in its primary coil. How many turns are in the secondary coil if the input voltage = 120V, and the output voltage = 6V
well, the ratio is 120:6 = 20:1 = 200:10
To determine the number of turns in the secondary coil of a step-down transformer, you need to use the turns ratio formula, which relates the number of turns in the primary coil (Np) to the number of turns in the secondary coil (Ns) and the voltage ratio (Vp/Vs).
The turns ratio formula is given by:
Np/Ns = Vp/Vs
In this case, the input voltage (Vp) is 120V, and the output voltage (Vs) is 6V.
So, substituting the values into the formula:
200/Ns = 120/6
First, simplify the right side:
200/Ns = 20
Now, cross-multiply:
20 * Ns = 200
Divide both sides by 20:
Ns = 200/20
Ns = 10
Therefore, the secondary coil has 10 turns.
To calculate the number of turns in the secondary coil of a step-down transformer, we can use the formula:
\( \frac{N_1}{N_2} = \frac{V_1}{V_2} \)
where \( N_1 \) and \( N_2 \) are the number of turns in the primary and secondary coils, respectively, and \( V_1 \) and \( V_2 \) are the input and output voltages, respectively.
Given that \( N_1 = 200 \), \( V_1 = 120V \), and \( V_2 = 6V \), we can substitute these values into the formula:
\( \frac{200}{N_2} = \frac{120}{6} \)
Simplifying the equation:
\( \frac{200}{N_2} = 20 \)
To isolate \( N_2 \), we can multiply both sides of the equation by \( N_2 \):
\( 200 = 20 \times N_2 \)
Next, divide both sides of the equation by 20:
\( 10 = N_2 \)
Therefore, there are 10 turns in the secondary coil of the step-down transformer.