Item 16

The voltage drop across R_{d} is 8V. What is the current across R_{e}?

a) 2A

b) 8A

c) 14A

d) 32A

Explanation:

This problem requires 3 electrical circuit concepts:

1) V=IR relating voltage, current, and resistance

2) The voltage drop across resistors in parallel is equal in each resistor

3) Kirchoff’s current law states that the sum of currents entering a node equals the sum of currents leaving a node

The voltage drop is equivalent for each resistor between red nodes A and B. The voltage drop across R_{d} is given as 8V, and therefore the voltage drop across resistors R_{b }and R_{c} is also 8V. Using V=IR for each resistor, the current in resistor R_{b}=4A, R_{c}=8A, and R_{d}=2A. Using Kirchoff’s current law at node B: 4A + 8A + 2A = 14A. The current leaving node B equals the current across R_{e} because there are no other nodes in between.

a) 2A, incorrect, this implies that the current across R_{d}=R_{e}.

b) 8A, incorrect, this implies that the current across R_{d} equals the voltage and the current across R_{e}.

c) 14A, correct.

d) 32A, incorrect, this answer incorrectly assumes a voltage of 8V across R_{e} and then uses a false relationship VR=I.