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If each of the two headlights uses 40 W and each of the two taillights 4 W , for a total of 88 W , how long will a fresh 12-V battery last if it is rated at 90 A⋅h ? Assume the full 12 V appears across each bulb. Express your answer using two significant figures.

Answer :

Answer:

12.27 h

Explanation:

Total power consumption by the car = 88 W

It has a battery of 12V and rating 90 A-h.

The full 12V appears across each bulb. We know that power is given by

[tex]P=Vi[/tex]

where, [tex]i[/tex] is the current flowing through the circuit.

So, in this case,

[tex]i=\frac{P}{V}=\frac{88}{12}A=7.3333A[/tex]

The rating in units of A-h is the amount of energy available in a battery that will allow a current of 1 A to flow in a circuit for 1 hour.

Naturally, the time for which the battery will last = [tex]\frac{90}{7.3333}h=12.27h[/tex]

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