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{"ops":[{"insert":"A rechargeable battery has "},{"insert":{"katex":{"formula":"emf_{\u03b5battery}","isBlock":false}}},{"insert":{"katex":{"formula":"=14.0V","isBlock":false}}},{"insert":", internal resistance\u00a0"},{"insert":{"katex":{"formula":"r=4.00\\Omega","isBlock":false}}},{"insert":" and battery capacity (total charge)\u00a0"},{"insert":{"katex":{"formula":"2.00 Ah","isBlock":false}}},{"insert":".\nWhen the battery is fully charged, a light bulb is connected to it for 8 hours (see picture above). The light bulb has specs\u00a0"},{"insert":{"katex":{"formula":"14.00V","isBlock":false}}},{"insert":" and\u00a0"},{"insert":{"katex":{"formula":"1.00W","isBlock":false}}},{"insert":". We assume the light bulb has constant resistance (independent of the current) and the emf of the battery remains constant.\nAfter these 8 hours the battery is disconnected from the light bulb and connected in this circuit for charging:\nThe charger consists of a ideal voltage source with "},{"insert":{"katex":{"formula":"emf_\u03b5=20.0 V","isBlock":false}}},{"insert":" \u00a0(with no internal resistance) and a resistor\u00a0"},{"insert":{"katex":{"formula":"R_1","isBlock":false}}},{"insert":" \u00a0in series.\n(a)\u00a0What is the minimum time that is needed to fully recharge the battery (with\u00a0"},{"insert":{"katex":{"formula":"R_1=0\\Omega","isBlock":false}}},{"insert":")\n(b)\u00a0What should the resistance\u00a0"},{"insert":{"katex":{"formula":"R_1","isBlock":false}}},{"insert":" \u00a0be to fully recharge the battery in exactly 1 hour?\n\n"}]}

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