Charge in the battery after charging for a certain time

In summary, the question involves finding the charge held by a rechargeable battery after 10 hours when connected in a circuit with an ideal 9V battery and resistors. The total equivalent resistance needs to be calculated using the formula 1/Req = 1/R1 + 1/R2 + 1/R3 + ... The current passing through the total equivalent resistance can be found using the equation V = IR. The charge held by the battery after 10 hours can be calculated using the formula Charge = Current x Time. The final result is that the battery would be approximately 87.2% charged after 10 hours.
  • #1
nobrainer612
26
0

Homework Statement



An ideal 9V battery is connected to a resistive divider consisting of a 330 Ohm and a 600Ohm resistor. A 1.5V rechargeable battery in series with a 1.5k Ohm resistor is connected in parallel with the 330 Ohm resistor. The battery has a capacity of 1200mAh and is half charged. How much charge does it hold after 10 hours?

9kuic5.jpg


Homework Equations



V=R*i

battery charging time = capacity of the battery / charging current power output of the charger:
hr = mAh / mA

AAA – AA – C – D sizes rechargeable batteries:
hours ( charging time ) equals to 12 x Ahr OR 12/100 x mAh ( 12/100 x mAh = hrs )

Power = V*i

The Attempt at a Solution



I tried to find the current going to the 1.5k Ohm dc source. I first combined the R1 and Ri2(internal) as parallel.

1/Req = 1/330 + 1/1500
Req= 270.5

Then I combined R1 to Req since they are in series:

270.5 + 600 = 870.5 Ohm

The the total Req is 870.5 Ohm

Then I tried to find the current passing through the total Req:

V=Ri
i=9V/870.5
i=0.01033

Then I will use the equation:
battery charging time = capacity of the battery / charging current power output of the charger:
= 1200mAH/0.01033
= 116166 .. wow

At this point I am totally confused. Since this is such a large number, I feel like I am doing it wrong.

Any help is appreciated.
 
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  • #2




Thank you for posting your question. It seems like you have made some good progress in finding the total equivalent resistance and the current passing through it. However, there are a few things that need to be clarified in order to accurately calculate the charge held by the rechargeable battery after 10 hours.

Firstly, the equation you have used to find the battery charging time is not applicable in this case. This equation is used for calculating the charging time of a battery using a charger, not for a battery connected in a circuit.

Secondly, the value you have calculated for the total equivalent resistance is incorrect. The correct way to combine resistors in parallel is by using the equation: 1/Req = 1/R1 + 1/R2 + 1/R3 + ... where R1, R2, R3, etc. are the individual resistances. In this case, it would be: 1/Req = 1/330 + 1/600 + 1/1500 = 0.00581. Therefore, Req = 172.27 Ohms.

Now, to find the current passing through the total equivalent resistance, we can use the equation V = IR. Since we know that the voltage across the total equivalent resistance is 9V, we can calculate the current as follows:

I = V/Req = 9V/172.27 Ohms = 0.0523A

This is the current passing through the total equivalent resistance, which includes the 330 Ohm resistor, the rechargeable battery, and the 1.5k Ohm resistor in parallel with the 330 Ohm resistor.

To calculate the charge held by the rechargeable battery after 10 hours, we can use the equation: Charge = Current x Time. Therefore, the charge held by the battery after 10 hours would be:

Charge = 0.0523A x 10 hours = 0.523Ah = 523mAh

This is the charge held by the battery after 10 hours. Since the battery has a capacity of 1200mAh and is half charged, the total charge it can hold is 600mAh. Therefore, after 10 hours, the battery would be approximately 87.2% charged (523mAh/600mAh x 100%).

I hope this helps clarify your doubts. If you have any further questions, please feel free to ask. Good luck with
 

1. How long does it take to fully charge a battery?

The amount of time it takes to fully charge a battery depends on the type of battery and the charging method. Generally, it can take anywhere from 1-12 hours to fully charge a battery.

2. Can I overcharge a battery?

Yes, overcharging a battery can lead to damage and reduce its lifespan. It is important to monitor the charging process and disconnect the battery once it is fully charged.

3. How do I know when a battery is fully charged?

Most devices and chargers have indicators that show when a battery is fully charged. You can also use a multimeter to measure the voltage of the battery, which should reach its maximum value when fully charged.

4. Is it okay to use my device while it is charging?

In most cases, it is safe to use your device while it is charging. However, it may cause the charging process to take longer or put additional strain on the battery.

5. How often should I charge my battery?

It is recommended to charge your battery whenever it reaches 20-30% capacity to prolong its lifespan. It is not necessary to fully discharge the battery before charging it again.

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