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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Two circular metal plates with 15 cm radius are connected to either side of a 75 V battery. The plates are separated by 5 mm. The battery is then disconnected and replaced with a wire that has a resistance 500 kiloohms.
(a) Calculate the charge that the battery sends to each plate.(b) Calculate how long it will take the capacitor to discharge to 2 nC.
capacitor and take C = xe A/d and Q = CAV to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.6 x 10-8 m, axon radius r = 2.0 x 10¹ μm, and
cell-wall dielectric constant x = 2.2.
Positive
charge
layer
Negative {
charge
layer
External fluid
Axon wall membrane
1
O No
O
Internal fluid
Axon radius = r
+
d
Q
(a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. (Assume an initial potential difference of 7.0 x 10-2 v.)
C
How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 x 10-2 V?
K+ ions
Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per angstrom squared (A2). An atom has a cross section of about 1 A²
(1 A = 10-10 m). (Compare to normal atomic spacing of one atom every few A.)
Yes
When is a 1.5 V AAA battery not actually a 1.5 V battery? That is, when do its terminals provide a potential difference of less than 1.5 V?
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