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Ohm's Law in Scalar Form

Figure shows ...

Question

Figure shows a part of a circuit. If a current of $12 m A$ exists in the $5 k Ω$ resistor, find the currents in the other three resistors. What is the potential difference between the points $A$ and $B$ ?

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Solution

$i_{1} \times 20 = i_{2} \times 10$
$\Rightarrow \frac{i_{1}}{i_{2}} = \frac{10}{20} = \frac{1}{2}$

$i_{1} = 4 m A, i_{2} = 8 m A$
current in $20 K Ω$ resistor $= 4 m A$
Current in $10 K Ω$ resistor $= 8 m A$
Current in $100 K Ω$ resistor $= 12 m A$
$V = V_{1} + V_{2} + V_{3}$
$V = 5 K Ω \times 12 m A + 10 K Ω \times 8 m A + 100 K Ω \times 12 m A$
$V = 60 + 80 + 1200 = 1340$ volts.

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