The output voltage of a charger should be

Question

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Option B: higher than the battery voltage

Explanation & Concepts:
To charge a battery, the charging source must provide a potential difference higher than the electromotive force (EMF) of the battery to overcome its internal resistance and drive current into it. If the charger output voltage were equal to or less than the battery voltage, no current would flow from the charger into the battery.

Working Principle: The charging process is governed by the relation $V_{charger} = E_{battery} + I_{charger} \cdot R_{internal}$, where $I_{charger}$ is the charging current. By maintaining $V_{charger} > E_{battery}$, a positive current flows from the positive terminal of the charger to the positive terminal of the battery. As the battery state-of-charge increases, its terminal voltage rises, necessitating a charger that can either maintain a constant higher potential or adjust its output accordingly.

Key Formulas: $V_{ch} = E_b + I \cdot R_i$ — where $V_{ch}$ is charger voltage, $E_b$ is battery EMF, and $R_i$ is internal resistance.; $P_{in} = V_{ch} \cdot I$ — representing the power delivered by the charger during the charging cycle.

Key Points: Charging current direction is from the higher potential point (charger) to the lower potential point (battery).; Internal resistance $R_i$ causes a voltage drop that must be compensated for during charging.; If $V_{charger} = E_{battery}$, the charging current becomes zero, reaching a state of equilibrium.; Overcharging occurs if the voltage is maintained at an excessively high level for too long.

Advantages: Ensures effective energy transfer to chemical cells.; Allows for controlled charging rates by varying the potential difference.

Disadvantages: Higher voltage creates heat loss due to internal resistance ($I^2R$ loss).; Potential risk of gassing or electrolyte breakdown if voltage is poorly regulated.

Applications: Lead-acid battery charging in automobiles.; Li-ion battery management systems (BMS) in portable electronics.

Additional Info: Constant Current (CC) and Constant Voltage (CV) are standard charging profiles used to manage this voltage relationship.. Option A is incorrect because current would flow out of the battery into the charger (discharging). Option C is incorrect as no net charging current would flow.

Answer: B is correct — the charger output voltage must exceed the battery voltage to ensure a net current flow into the battery terminals.

Exam Tip: Always remember that in electrical circuits, current flows from higher potential to lower potential; thus, for charging, the source must always be at a higher potential than the sink.

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Option A: less than the battery voltage

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Option C: the same as the battery voltage

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Option D: none of the above

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