A 12V 1.5 ohm battery connected to a ____ ohm load yields maximum power transfer.
Answers
A 12V 1.5 ohm battery connected to a 1.5 ohm load yields maximum power transfer.
Step-by-step explanation:
Given:
A 12V battery has internal resistance of 1.5 ohm
To find out:
The resistance that it should be connected to yield the maximum power
Solution:
We know that maximum power is supplied when the load resistance is equal to the source resistance
Therefore, a 12V 1.5 ohm battery connected to a 1.5 ohm load yields maximum power transfer
Hope this answer is helpful.
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Given : 12V 1.5 ohm battery connected to a load
To Find : load yields maximum power transfer.
Solution:
12V
1.5 Ω
Load = R Ω
I = V/ R
=> I = 12/(R + 1.5)
maximum power transfer P is max
P = I² R
Substitute I = 12/(R + 1.5)
P = ( 12/(R + 1.5))² R
=> P = 144R/(R + 1.5)²
dP/dR = 144R (-2)/(R + 1.5)³ + 144/(R + 1.5)²
dP/dR = 0
=> 144R (-2)/(R + 1.5)³ + 144/(R + 1.5)² = 0
=> -2R + R + 1.5 = 0
=> R = 1.5
dP/dR = 144R (-2)/(R + 1.5)³ + 144/(R + 1.5)²
= (-288R + 144R + 216)/(R + 1.5)³
= (216 - 144R)/(R + 1.5)³
d²P/dR² = (216 - 144R)(-3)/(R + 1.5)⁴ + (-144)/(R + 1.5)³
Put R = 1.5
=> d²P/dR² = 0 - 144/27
=> d²P/dR² < 0
Hence R = 1.5 will give maximum power
12V 1.5 ohm battery connected to a __1.5__ ohm load yields maximum power transfer.
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