Question

8. Three resistors of 1ohm,2hom and 4ohm are
connected in parallel in a circuit. If a 1 resistor draws a current
of 1 A, find thecurrent through the other two resistors.​

Answer 1

▶ Solution :

Given :

▪ Three resistors of 1Ω, 2Ω and 4Ω are connected in parallel in a circuit.

▪ Current passed through resistor of resistance 1Ω = 1A

To Find :

▪ Current passed through the other two resistors.

Concept :

☞ First we have to calculate potential difference across the parallel connection.

☞ We can calculate potential difference with the help of ohm's law.

☞ As per ohm's law current passed through a conductor is directly proportional to the applied potential difference.

Mathematically,

$\boxed{\bf{\red{V\propto I}}}$

• V denotes potential difference
• I denotes current

Calculation :

1) Potential difference across connection :

$\implies\sf\:V=I_1R_1\\ \\ \implies\sf\:V=1\times 1\\ \\ \implies\bf\blue{V=1\:volt}$

2) Current passed through 2Ω resistor :

$\implies\sf\:V=I_2R_2\\ \\ \implies\sf\:1=2I_2\\ \\ \implies\bf\pink{I_2=0.5\:A}$

3) Current passed through 4Ω resistor :

$\implies\sf\:V=I_3R_3\\ \\ \implies\sf\:1=4I_3\\ \\ \implies\bf\orange{I_3=0.25\:A}$

Answer 2

Aɴꜱᴡᴇʀ

➜ Current through the 2Ω resistor = 0.5 A

➜ Current through the 4Ω resistor = 0.25 A

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Gɪᴠᴇɴ

➤ Three resistors each of 1Ω, 2Ω , 4Ω are connected parallely

➤ Current (A) through the resistor of 1Ω is 1A

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ᴛᴏ ꜰɪɴᴅ

Current through the other 2 resistors

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Sᴛᴇᴘꜱ

❍ In a Parallel Connection of resistors the current through each resistor is not the same.

So we will have to find current through each resistor seperately and to do that we use Ohm's law(V=IR)

Here we know the value of R and the current through the 1Ω resistor so let's first find the voltage.

1) Potential difference across connection :

$\begin{lgathered}\leadsto\rm\:V=I_1R_1\\ \\ \leadsto\rm\:V=1\times 1\\ \\ \leadsto\sf\pink{V=1\:volt}\end{lgathered}$

☞ Voltage accross any point in a circuit is always the same(Does not matter if it's a parallel or a series connection)

So now the current accross the other 2 resistors is,

$\begin{lgathered} \sf{} \bigstar{} Current \: through \: the \: 2Ω \: resistor \\ \\ \mapsto\tt\:V=I_2R_2\\ \\ \mapsto\tt\:1=2I_2\\ \\ \pink{ \dashrightarrow\rm{I_2=0.5\:A}} \\ \\ \sf{} \bigstar{} Current \: through \: the4 Ω \: resistor \\ \\ \hookrightarrow\tt\:V=I_3R_3\\ \\ \hookrightarrow\tt\:1=4I_3\\ \\ \pink{\hookrightarrow\rm{I_3=0.25\:A}}\end{lgathered}$

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