Three resistors take the shape of a triangle,one resistor in each leg.Resistance in one leg is 4 ohms,in a second leg is 6 ohms,and third leg is 10 ohms.A measurement of resistance across the 10-ohm resistor will show the equivalent resistance to be
A)1.4 ohms.
B)5 ohms.
C)6.7 ohms.
D)greater than 6.7 ohms.

Question

Quizplus · Accepted Answer

The resistors form a triangle, meaning the 4-ohm and 6-ohm resistors are in parallel with each other and this combination is in series with the 10-ohm resistor. The equivalent resistance of the 4-ohm and 6-ohm resistors in parallel is (4*6)/(4+6) = 24/10 = 2.4 ohms. Adding this to the 10-ohm resistor gives a total of 12.4 ohms. However, the question asks for the measurement across the 10-ohm resistor, which means looking at the parallel combination of the 4-ohm and 6-ohm resistors from the perspective of the 10-ohm resistor. This is a misunderstanding in my explanation; the correct interpretation should focus on the equivalent resistance seen across the 10-ohm resistor, which involves calculating the parallel resistance of the 4-ohm and 6-ohm resistors, effectively bypassing the 10-ohm resistor for this specific measurement scenario. The correct calculation for the equivalent resistance seen across the 10-ohm resistor involves the parallel combination of the 4-ohm and 6-ohm resistors, which indeed results in a lower resistance value, reflecting the combined paths for current around the 10-ohm resistor, not adding it to the series.

Three Resistors Take the Shape of a Triangle,one Resistor in Each