Question

The total charge a battery can supply is rated in mA⋅hmA⋅h, the product of the current (in mA) and the time (in h) that the battery can provide this current. A battery rated at 1000mA⋅h can supply a current of 1000 mA for 1.0 h, 500 mA current for 2.0 h, and so on. A typical AA rechargeable battery has a voltage of 1.2 V and a rating of 1800mA⋅h. For how long could this battery drive current through a long, thin wire of resistance22Ω?

Answer 1

To determine how long a 1.2 V, 1800mAh AA battery can drive current through a 22Ω wire, calculate the current using Ohm's law and then divide the total battery charge by this current, which results in approximately 33.03 hours.

Step-by-step explanation:

The student is asking how long a rechargeable AA battery with a voltage of 1.2 V and a charge capacity of 1800mAh can supply current through a wire with a resistance of 22Ω. To answer this, we use Ohm's law which states that current (I) = voltage (V) / resistance (R). So, the current the battery can supply through this wire would be 1.2V / 22Ω, which is approximately 0.0545A or 54.5mA. The total charge the battery can supply is then divided by the current to find the time the battery can last: 1800mAh / 54.5mA = approximately 33.03 hours.

Answer 2

118800 seconds

Step-by-step explanation:

Given :

Voltage, V = 1.2 V

Resistance, R = 22 Ω

Applying Ohm's law, we get

Voltage, V = IR

Current
`$I=(V)/(R)$`

`$I=(1.2)/(22)$`

I = 0.0545 A

Rate = 1800 mAh

Time taken,
`$t=(1800 * 10^(-3))/(0.0545)$`

= 33 hr

= 118800 s