University Physics Volume 2
University Physics Volume 2
18th Edition
ISBN: 9781938168161
Author: OpenStax
Publisher: OpenStax
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Chapter 10, Problem 10.1CYU

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
Check Mark
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=( ε r)2r=εr2

Conclusion:

Power dissipated in the internal resistance will generate heat, and the battery begins to get hot.

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Chapter 10 Solutions

University Physics Volume 2

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