In an electrical circuit, the three resistors of \( 3\,\Omega \), \( 6\,\Omega \) and \( 9\,\Omega \) are connected in series. The voltage drop across \( 3\,\Omega \) is 5 V. The voltage drop across the combination is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 30\,\mathrm{V} \)
In a series circuit the same current flows through every resistor, so the current follows from the \( 3\,\Omega \) resistor, and the voltage across the combination is that current times the total resistance.
\( \displaystyle I = \frac{V_1}{R_1} = \frac{5}{3}\,\mathrm{A} \)
\( \displaystyle R_{\mathrm{total}} = 3 + 6 + 9 = 18\,\Omega \)
\( \displaystyle V = I\,R_{\mathrm{total}} = \frac{5}{3} \times 18 = 30\,\mathrm{V} \)
Shortcut: In series the voltage divides in the ratio of the resistances, \( 3 : 6 : 9 = 1 : 2 : 3 \). The \( 3\,\Omega \) resistor takes 1 part out of 6, so the total is \( 6 \times 5\,\mathrm{V} = 30\,\mathrm{V} \).