Inverter backup that does not match the dealer's promise
A family in Cuttack runs their home during power cuts on a 12 V, 150 Ah tubular lead-acid battery with a 700 VA inverter. During a four-hour outage they switch on two ceiling fans of 75 W each, three LED lamps of 9 W each and a 40 W television. The dealer who sold the set promised 'about six hours of backup'. In practice the lights begin to dim at about three and a half hours and the inverter starts beeping. The battery is three years old, the terminals carry a white crust, and the cable lug near the positive terminal feels warm after an hour of running. The family now wants to run a 0.5 HP (373 W) water pump from the same inverter during outages. The data sheet gives the inverter efficiency as 85% and warns against discharging the battery below 50% of its rated capacity if the rated 1200 cycles are to be approached.
1. Using the nameplate figures, estimate the backup time down to 50% depth of discharge and decide whether the battery is faulty or the promise was wrong.
Read the worked answer
Load = (2 × 75) + (3 × 9) + 40 = 150 + 27 + 40 = 217 W.
Usable energy stored at 50% depth of discharge = 12 V × 150 Ah × 0.5 = 900 Wh.
Energy actually delivered to the loads after inverter losses = 900 × 0.85 = 765 Wh.
Backup = 765 Wh ÷ 217 W ≈ 3.5 hours.
This is almost exactly what the family observes, so the battery is behaving roughly like a healthy battery of that rating. The 'six hours' figure comes from dividing the full 1800 Wh by 217 W (≈ 8.3 h) and then rounding down without allowing for either the inverter loss or the depth-of-discharge limit. The dimming and beeping near the end are not a separate fault: as the battery empties, its terminal voltage sags under a current of about 18 A, and an aged battery has higher internal resistance, so the inverter's low-voltage cut-off operates slightly early. The correct conclusion is a specification error, not a failed cell.
2. Should the family add the 0.5 HP pump to this inverter and battery? Support your answer with numbers.
Read the worked answer
New load = 217 + 373 = 590 W.
DC current drawn from the battery = 590 ÷ (0.85 × 12) ≈ 58 A. On a 150 Ah battery that is a discharge rate of about 0.39C, far above the gentle rate at which the rated capacity is measured; the delivered capacity falls sharply, so the real backup would be well under the 765 ÷ 590 ≈ 1.3 hours the arithmetic suggests.
Inverter rating: 590 W at a power factor of about 0.8 is roughly 737 VA, already above the 700 VA nameplate, and a motor draws two to three times its running current for a second or two at start-up. The inverter will trip on overload or shut down.
A 58 A draw also heats the already corroded terminals and cables.
Verdict: do not add the pump. A pump runs for only 10–20 minutes at a time; a separate small DC pump, a hand pump, or running the pump only when mains power is present is the sensible arrangement. Replacing the battery with a larger one would help capacity but would not fix the undersized inverter.
3. The terminals are crusted white and the lug feels warm. Explain what is happening and the correct remedy.
Read the worked answer
The white crust is lead sulphate formed when acid mist creeps up the post and reacts with the lead; it is an insulator, so the contact resistance between post and lug rises. Every joint has a resistance, and heat produced goes as I²R. At around 20 A a joint of even a few hundredths of an ohm dissipates several watts, which is why the lug feels warm. Left alone it worsens: the insulation softens, the joint can arc, and a fire near a hydrogen-releasing battery is a real hazard. The voltage drop also makes the inverter cut off early.
Remedy, in order: switch off and disconnect the negative first; clean the post and lug with a paste of baking soda to neutralise acid, rinse with plain water and dry thoroughly; replace a badly eaten lug rather than reusing it; refit and tighten to the manufacturer's torque; smear petroleum jelly on the assembled joint to keep acid mist out. Check that the fuse fitted close to the positive terminal is rated for the cable, and that the cable cross-section suits the current. Never work on the terminals with the inverter on.