# Question #c3b78

Jan 29, 2016

I would go for B) zero to $7.5 V$

#### Explanation:

The variable resistor can be set (I think) starting at zero up to $50 k \Omega$.

At zero (basically the resistor becomes a simple wire) the voltage drop between points P and Q is zero (or the difference in potential between them is zero).

When at $50 k \Omega$ we can use Ohm`s Law:
$V = R i$
to find the current in the circuit comprising the series of the two resistors:
$i = \frac{V}{R} = \frac{9}{10 k \Omega + 50 k \Omega} = 1.5 \times {10}^{-} 4 A$
and again to find the voltage drop across the variable resistor (at $50 k \Omega$):
${V}_{P Q} = 50 k \Omega \cdot 1.5 \times {10}^{-} 4 A = 7.5 V$