Sample MCAT question: Voltage drop across resistors

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The voltage drop across Rd is 8V. What is the current across Re?

a) 2A

b) 8A

c) 14A

d) 32A

Solution

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 Rd is given as 8V, and therefore the voltage drop across resistors Rb and Rc is also 8V. Using V=IR for each resistor, the current in resistor Rb=4A, Rc=8A, and Rd=2A. Using Kirchoff’s current law at node B: 4A + 8A + 2A = 14A. The current leaving node B equals the current across Re because there are no other nodes in between.

a) 2A, incorrect, this implies that the current across Rd=Re.

b) 8A, incorrect, this implies that the current across Rd equals the voltage and the current across Re.

c) 14A, correct.

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