Question

What is the effective resistance between the points A and D? A) 1.3 Ω B) 2.2 Ω C) 10 Ω D) 12 Ω

Answer 1

B) 2.2 Ω

Step-by-step explanation:

The resistor between B and C is connected in parallel to the resistor between C and D (because their ends are connected to the same points: C on one side and B (which has same voltage as D) on the other side, so they have same potential difference across them.

So their equivalent resistance is

`(1)/(R_(BD))=(1)/(R_(BC))+(1)/(R_(CD))=(1)/(4.0 \Omega)+(1)/(5.0 \Omega)=(9)/(20 \Omega)\\R_(BD)=(20 \Omega)/(9)=2.22 \Omega`

The resistor between A and B, instead, is short-circuited, because the current flows through the upper branch of the circuit (connecting A with C), which has zero resistance (it is a wire without any resistor). This means that the resistor between A and B should not be considered: so, the total resistance of the circuit is

`2.2 \Omega`