Question

The total charge a battery can supply is rated in mA*h, the product of the current (in mA) and the time (in h) that the battery can provide this current. A battery rated at 1000 mA*hr 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 1800 mA*h.
A) For how long could this battery drive current through a long, thin wire of resistance 28 Ω ?

Answer 1

Answer:

42 hours

Explanation:

Given:

Voltage of AA battery (V) = 1.2 V

Charge rating of the battery (QR) = 1800 mA·h

Resistance of the wire (R) = 28 Ω  

Let the time taken by the battery be 't' hours.

Now, from the definition of Ohm's law, we know that, voltage is directly proportional to the current drawn and is given as:

$V=IR\\Where,I\to Current\ drawn$

Rewriting in terms of 'I', we get:

$I=\frac{V}{R}$

Plug in the given values and solve for 'I'. This gives,

$I=\frac{1.2}{28}=\frac{3}{70}\ A$

Now, let us convert current from A to mA using the conversion factor.

1 A = 1000 mA

$\frac{3}{70}\ A=\frac{3}{70}\times 1000=\frac{300}{7}\ mA$

Now, from the definition of charge rating, we have:

Charge rating = Current drawn (mA) × Time taken (h)

$QR=I\times t\\\\t=\frac{QR}{I}$

Plug in the given values and solve for 't'. This gives,

$t=\frac{1800\ mA\cdot h}{\frac{300}{7}\ mA}\\\\t=\frac{126}{3}=42\ h$

Therefore, the battery could drive the current through the long thin wire for 42 hours.