Chapter 21, Problem 78GP

To determine

The primary windings of a transformer which has an 80% efficiency are connected to 110-v ac.

Answer to Problem 78GP

Solution:

a)The current through primary windings of the transformer.

b)The secondary voltage is calculated from the secondary power and resistance.

Explanation of Solution

Given:

Primary voltage $V_1=110V$

Efficiency of transformer $e=0.8$

Wattage rating of bulb $P_2=75W$

Resistance of bulb $R=2.4\Omega$

Formula used:

$I_1=\frac{P_2}{e{V}_1}$

Calculation:

a) The current through primary windings of the transformer.:

Primary voltage $V_1=110V$

Efficiency of transformer $e=0.8$

Wattage rating of bulb $P_2=75W$

Resistance of bulb $R=2.4\Omega$

$\begin{array}{l}{P}_2=e{P}_1\\ P_2=e{I}_1{V}_1\\ I_1=\frac{P_2}{e{V}_1}\\ I_1=\frac{75}{0.8\times 110}A\\ I_1=0.852A\end{array}$

b)The secondary voltage is calculated from the secondary power and resistance.:

Secondary voltage

$\begin{array}{l}P=\frac{V_s{}^2}{R}\\ \frac{N_p}{N_S}=\frac{V_p}{V_S}=\frac{V_p}{\sqrt{P_s{R}_s}}\\ =\frac{110V}{\sqrt{\left(75W\right)\left(2.4\Omega \right)}}\\ or\frac{N_p}{N_s}=8.2\end{array}$