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Given: • A 55 VDC parking lot light (on only at night) consumes 24 W when on • It is powered by a 55 VDC battery which is recharged by a solar panel • The 111 W solar panel only generates 12 VDC, so an inverter is used to boost the voltage to 55 VDC to recharge the battery • The inverter is 90% efficient (output power is 90% of input power) • After four particularly cloudy days (were the solar panel was unable to recharge the battery), the solar panel is finally able to recharge the half discharged battery to full in 4.2 hours What is the rated capacity of the 55 VDC battery (in Ah)? Answer tolerance is 5%.

Given: • A 55 VDC parking lot light (on only at night) consumes 24 W when on • It is powered by a 55 VDC battery which is recharged by a solar panel • The 111 W solar panel only generates 12 VDC, so an inverter is used to boost the voltage to 55 VDC to recharge the battery • The inverter is 90% efficient (output power is 90% of input power) • After four particularly cloudy days (were the solar panel was unable to recharge the battery), the solar panel is finally able to recharge the half discharged battery to full in 4.2 hours What is the rated capacity of the 55 VDC battery (in Ah)? Answer tolerance is 5%.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Given: A 55 VDC parking lot light (on only at night) consumes 24 W when on • It is powered by a 55 VDC battery which is recharged by a solar panel The 111 W solar panel only generates 12 VDC, so an inverter is used to boost the voltage to 55 VDC to recharge the battery • The inverter is 90% efficient (output power is 90% of input power) • After four particularly cloudy days (were the solar panel was unable to recharge the battery), the solar panel is finally able to recharge the half discharged battery to full in 4.2 hours What is the rated capacity of the 55 VDC battery (in Ah)? Answer tolerance is 5%.
Transcribed Image Text:Given: A 55 VDC parking lot light (on only at night) consumes 24 W when on • It is powered by a 55 VDC battery which is recharged by a solar panel The 111 W solar panel only generates 12 VDC, so an inverter is used to boost the voltage to 55 VDC to recharge the battery • The inverter is 90% efficient (output power is 90% of input power) • After four particularly cloudy days (were the solar panel was unable to recharge the battery), the solar panel is finally able to recharge the half discharged battery to full in 4.2 hours What is the rated capacity of the 55 VDC battery (in Ah)? Answer tolerance is 5%.
Expert Solution
Step 1

The 55 V DC battery is half discharged. It takes 4.2 hours to recharge the half-discharged battery. So, it takes 8.4 hours to fully charge. Now, the solar panel output power is 111 W. It is connected to the inverter. The inverter is 90% efficient.

The output of the inverter is,

Pout=η×Pin=90%×111=0.9×111=99.9 W

The inverter output power is used as input to charge the 55 VDC.

The charging current of the battery is,

I=PoutVDC=99.955=1.816 A

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