Each of the resistors in a circuit is 3 ohms. If the current in the middle resistor is zero what is the equivalent resistance?

Answer 1

First, the question doesn't say if the resistors are in series or parallel, or series-parallel. Second, the current given is zero, which can only be true if the circuit has no applied voltage. (It's turned off.) This will be true regardless of the circuit configuration. We were told the "middle resistor" in the question, but that's still a bit "iffy" for us. We need to know how it's wired. Since we don't, we'll look at the three possibilities. If all three resistors are in series, the total resistance is the sum of all the resistors. It's this: Rt = R1 + R2 + R3 ... or Rt = 3 + 3 + 3 = 9 ohms A shortcut can be applied when identical resistors are in series. The total resistance will be the value of one multiplied by the number of them in series. In this case, 3 x 3 = 9 ohms. If the resistors are all in series, the total resistance is this: Rt = 1 / ( {1 / R1} + {1 / R2} + {1 / R3} ...) or Rt = 1 / ( {1/3} + {1/3} + {1/3}) = 1 / (3/3) = 1 / 1 = 1 ohm We can shortcut that when we have identical resistors in parallel. The total resistance will be the value of one of them divided by the number that are in parallel. So we'd have: Rt = (3 / 3) = (1 / 1) = 1 ohm If two are in series with one across them in parallel, the total resistance is found for each individual parallel branch and then the parallel branches (which have been reduced to a single equivalent resistance) can be taken into the parallel resistors equation and the total equivalent resistance calculated. In this case, one branch has two series resistors of three ohms. The total for that branch is 6 ohms, which we find by just adding them up. Now we have a 6 ohm (equivalent) resistor in parallel with a 3 ohm resistor. Take them into the equation and calculate. It's like this: Rt = 1 / ({1/6 } + { 1/3 }) = 1 / ({ 1/6 } + { 2/6 }) = 1 / ( { 3/6 }) = 1/ (1/2) = 2 ohms