Chapter 7, Problem 10STP

To determine

To calculate: The voltage in the output coil and current in the light.

Answer to Problem 10STP

Voltage in the output coil is $\underset{\_}{12\text{ V}}$ .

Current in the light is $\underset{\_}{1.5\text{ A}}$ .

Explanation of Solution

Given:

Input voltage = $\text{120 V}$

Number of turns in primary coil = $\text{20}$

Number of turns in secondary coil = $\text{2}$

Resistance of the bulb = $\text{8 }\Omega$

Formula used:

Transformer voltage equation is given by,

  $\frac{V_{\text{out}}}{V_{\text{in}}}=\frac{N_2}{N}$

Where $V_{\text{out}}$ is output voltage, $V_{\text{in}}$ is input voltage, $N_2$ turns in secondary coil and $N$ is turns in primary coil.

Current is given by,

  $I=\frac{V}{R}$

Where $V$ is voltage and $R$ is resistance.

Calculation:

Voltage in the output coil is calculated as:

  $\begin{array}{l}\frac{V_{\text{out}}}{V_{\text{in}}}=\frac{N_2}{N}\\ V_{\text{out}}=\frac{N_2}{N}\times V_{\text{in}}\\ =\frac{2}{20}\times 120\text{ V}\\ =12\text{ V}\end{array}$

Current in the light is calculated as:

  $\begin{array}{l}I=\frac{V}{R}\\ =\frac{12\text{ V}}{8\Omega }\\ \text{ = }1.5\text{ A}\end{array}$

Conclusion:

Voltage in the output coil is $\underset{\_}{12\text{ V}}$ .

Current in the light is $\underset{\_}{1.5\text{ A}}$ .