91影视

The resistance $r=1000\mathrm{ohm}$,

The resistance $R=10\mathrm{ohm}$,

A transformer is a device that transfers electrical energy from one alternating current circuit to one or more other circuits by either increasing (stepping up) or decreasing (stepping down) the voltage.

Use the relation between primary current, the number of turns in the primary coil, secondary current, and the number of turns in the secondary coil.

Then by using the formula for power,define the ratio of turns.

Formula:

$I_s=\frac{N_p{I}_p}{N_s}$

$P=I_s^{2}R$

$I_p=\frac{{蔚}_{rms}}{R_{eq}+r}$

The RMS current in secondary coil is as follows

$I_s=\frac{N_p{I}_p}{N_s}$

The primary current in circuit is given as,

$\begin{array}{rcl}{I}_p& =& \frac{{蔚}_{rms}}{R_{eq}+r}\\ & =& \frac{{蔚}_{rms}}{{\left(\frac{N_p}{N_s}\right)}^{2}R+r}\end{array}$

Then power equation is written as follows.

$P={\left(\frac{{蔚}_{rms}}{{\left(\frac{N_p}{N_s}\right)}^{2}R+r}\right)}^2{\left(\frac{N_p}{N_s}\right)}^{2}R$

Let鈥檚 assume

$x={\left(\frac{N_p}{N_s}\right)}^2$

$P_{avg}=\frac{{蔚}_{rms}^2脳R脳x}{{\left(xR+r\right)}^2}$

Then differentiate with respect to $x$:

$\begin{array}{rcl}\frac{d{P}_{avg}}{dx}& =& \frac{{蔚}_{rms}^2脳R脳\left(r-xR\right)}{{\left(xR+r\right)}^3}\\ & =& 0\end{array}$

$\frac{{蔚}_{rms}^2脳R脳\left(r-xR\right)}{{\left(xR+r\right)}^3}=0$

So,

$\begin{array}{rcl}x& =& \frac{r}{R}\\ & =& \frac{1000}{10}\\ & =& 100\mathrm{ohm}\end{array}$

But we know

$\begin{array}{rcl}x& =& {\left(\frac{N_p}{N_s}\right)}^2\\ {\left(\frac{N_p}{N_s}\right)}^2& =& 100\\ \frac{N_p}{N_s}& =& 10\end{array}$

Hence, number of turns ratio is 10.