Question

A rechargeable battery has $emf_{εbattery}$$=14.0V$, internal resistance $r=4.00\Omega$ and battery capacity (total charge) $2.00 Ah$.

When the battery is fully charged, a light bulb is connected to it for 8 hours (see picture above). The light bulb has specs $14.00V$ and $1.00W$. We assume the light bulb has constant resistance (independent of the current) and the emf of the battery remains constant.

After these 8 hours the battery is disconnected from the light bulb and connected in this circuit for charging:

The charger consists of a ideal voltage source with $emf_ε=20.0 V$  (with no internal resistance) and a resistor $R_1$  in series.

(a) What is the minimum time that is needed to fully recharge the battery (with $R_1=0\Omega$)

(b) What should the resistance $R_1$  be to fully recharge the battery in exactly 1 hour?

Answer 1

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