In the circuit diagram, a potentiometer with total resistance $120\ \Omega$ is connected in parallel with a resistor whose resistance is $150\ \Omega$ and a resistor of resistance $R$. The battery has electromotive force (e.m.f.) $12\ \text{V}$ and negligible internal resistance. The voltmeter shows $0\ \text{V}$ when the slider on the potentiometer is positioned $\frac{1}{4}$ of the distance up from its lower end, as illustrated. Determine the resistance $R$.
- A$30\ \Omega$
- B$38\ \Omega$
- C$50\ \Omega$
- D$450\ \Omega$