Three resistors take the shape of a triangle, one resistor in each leg. Resistance in one leg is 4 ohms, 6 ohms in a second leg, and a third leg 10 ohms. Connecting an ohm-meter 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 2.4 + 10 = 12.4 ohms. However, the question asks for the resistance measured 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 was a mistake in my calculation explanation; the correct approach is to consider how the resistors are connected and the perspective from which the measurement is taken. The correct calculation should consider the parallel and series connections correctly, focusing on the measurement across the 10-ohm resistor. The equivalent resistance seen across the 10-ohm resistor actually involves the parallel combination of the 4-ohm and 6-ohm resistors, which correctly calculated gives 2.4 ohms as the equivalent resistance of the parallel combination, but this is not the value measured across the 10-ohm resistor directly; the question's phrasing implies looking for an equivalent resistance incorporating the 10-ohm resistor's perspective in the circuit configuration, which was misunderstood in my explanation.

Three Resistors Take the Shape of a Triangle, One Resistor