Check Your Understanding If you place a wire directly across the two terminal of a battery, effectively shorting out the terminals, the battery will begin to get hot. Wiry do you suppose this happens?
Check Your Understanding If you place a wire directly across the two terminal of a battery, effectively shorting out the terminals, the battery will begin to get hot. Wiry do you suppose this happens?
Check Your Understanding If you place a wire directly across the two terminal of a battery, effectively shorting out the terminals, the battery will begin to get hot. Wiry do you suppose this happens?
Expert Solution & Answer
To determine
The reason for the battery getting heated while shorting out its two terminals.
Explanation of Solution
Introduction:
If a battery with internal resistor r is connected to a load resistor R, the load resistor is in series with the internal resistor. The equivalent resistance of the circuit becomes (r+R).
Applying Ohm's law in the circuit
The magnitude of the current flowing through the resistor is, I=εr+R, and
Power consumed by a resistor, P=V2R=I2R
Short circuit of battery occurs, if one connectsthe positive terminal of the battery to the negative terminal with highly conducting wire. Due to low load resistance, a huge amount of current starts to flow.
One can assume resistance of the connecting wire is zero, then the magnitude of the current flow through the circuit is
I=εR+r=ε0+r=εr
The power dissipated in internal resistance,
P=I2r=(εr)2r=εr2
Conclusion:
Power dissipated in the internal resistance will generate heat, and the battery begins to get hot.
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