Two resistors of resistances $10 Ω$ and $20 Ω$ are connected in parallel. A battery supplies $6 A$ of current to the combination. Calculate the current in each resistor.

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Solution

The current in the $10 Ω$ resistance is
$i_{1} = \frac{R_{2}}{R_{1} + R_{2}} i = \frac{(20) \times (6)}{20 + 10} = 4 A$
The current in the $20 Ω$ resistor is
$i_{2} = \frac{R_{1}}{R_{1} + R_{2}} i = \frac{10 \times 6}{10 + 20} = 2 A$
Or
emf across $10 Ω$ resistor
$V_{1} = i_{1} \times 10$
emf across $20 Ω$ resistor
$V_{2} = i_{2} \times 20$
Since $i_{1} + i_{2} = 6 A$ and $V_{1} = V_{2}$ , we have $i_{1} = 4 A$
$i_{2} = 2 A$

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Two resistors of resistances 10Ω and 20Ω are connected in parallel. A battery supplies 6A of current to the combination. Calculate the current in each resistor.

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