Discussion
For the following circuit, find the voltage needed across a - b terminal so that drop across the 10 Ω resistor is 20 V :
Answer: D
The voltage needed is 80 V.
With c-d open, the 30 Ω and 10 Ω resistors form one path from a to b (a to c through 30 Ω, then c to b through 10 Ω), and the 5 Ω resistor forms a second path from a to d, which is joined directly to b. The two paths are in parallel across a-b.
For 20 V across the 10 Ω resistor, the current in the 30 Ω and 10 Ω path is
\[ \begin{aligned} I &= \frac{20}{10} = 2\ \text{A} \\ V_{ab} &= 2 \times (30 + 10) = 80\ \text{V} \end{aligned} \]
The 5 Ω path draws its own current but does not change the voltage across the other path. 20 V is the drop across the 10 Ω resistor alone, and 60 V is the drop across the 30 Ω resistor alone.
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