A 3- resistoris connected in parallel with a 6- resistor. This pair isthen conne

Question

A 3- resistoris connected in parallel with a 6- resistor. This pair isthen connected in series with a 4- resistor. Theseresistors are connected to a battery. What will happen if the3- resistor breaks, i.e., becomes an infiniteresistance?

a) The current in the4- resistor will drop to zero.

b) The current in the6- resistor will increase.

c) The current provided bythe battery will not change.

Determine the best answer and explain your choice byinvoking the appropriate concept, principle, and/or mathematicalrelation.

Explanation / Answer

The answer is b, the current in the 6 resistor willincrease. I reached this conclusion due to the fact that since the 3 and6 ohm resistors are in parallel their equivalent resistance willbe: Req = (R1 x R2) / (R1 + R2) = 18 / 9 = 2 When you have the 6 and 3 in parallel, we know, by currentdivision, that the current through the 3 resistor is: I3 = (6/3+6)It =2/3Itot => or 2/3 the total current which means only1/3 flows through the 6. Itot = V/(2+4) = V/6 If we let V = 1 then Itot is 1/6A, with the 6carrying (1/6) x (1/3) = 1/18A When the 3 resistor blows now all of the current in thecircuit will flow through the 6 (and the 4 ofcourse). Now Itot = V/(6+4) = V/10 With V = 1 again Itot is 1/10A with boththe 6 and 4 carrying this current (since they are inseries). You can see how now the 6 carries 1/10A wherebefore it carried only 1/18A. Therefore the currentincreases. And by elimination: The answer cannot be a because you still have a path forcurrent to flow since the 6 and 4 ohm are now in series. The answer cannot be c because the current changes if theresistance changes. V=IR The answer cannot be d because after the 3 resistorblows you have more resistance in the circuit, 10, whichmeans you have less current and therefore less power sinceP=IV.

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