Question

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

Answer 1

Answer:

Given

$\sf{ \bull R_1=1Ω} \\ \sf{ \bull R_2=2Ω} \\ \sf{ \bull R_3= 4Ω }$

$\sf{ \bull current\: passing \: through \: 1Ω \: resistor \: is \: 1A}$

--------------------------------------------------

To find

Current passing through 2Ω and 4Ω.

--------------------------------------------------

Concept used.

~Here the concept of Ohm's Law is used. First we will find the voltage across the all resistors by using V= IR. Then will separately calculate the current flowing through the 2Ω and 4Ω using V= IR.

----------------------------------------------------

Solution

»In parallel combination the current is different in the resistors but the voltage across the each resistor is same.

»According to ohm's law

${ \underline{ \boxed{ \sf{V= IR}}}}$

where

• v denotes voltage
• I denotes current
• R denotes resistance

$\sf{ \implies V= 1 × 1} \\ \\ \sf{ \implies \red{V= 1 \: Volt }}$

»So the voltage across all resistors in the circuit is 1 Volt.

___________________________

Current passing through 2Ω resistor:-

$\sf{ \to \green{ V= IR \: (by \: ohm's \: law)}}$

$\sf{ \implies I =\frac{V}{R}}\\ \\ \sf{ \implies I = \frac{1}{2}} \\ \\ \sf{ \implies \orange{ I= 0.5 A} }$

»So the current flowing through 2Ω resistor is 0.5 Ampere.

___________________________

»Current passing through 4 Ω resistor:-

$\sf{ \to \orange{V= IR \:( by \: Ohm's \: law)}}$

$\sf{ \implies I= \frac{V}{R} }\\ \\ \sf{ \implies I= \frac{1}{4}} \\ \\ \sf{ \implies \pink{I= 0.25 A}}$

»So the current flôwing through the 4Ω resistor is 0.25 Ampere.

-----------------------------------------------------

More to know !!

■ Ohm's law - the current passing through a metallic element is directly proportional to the potential difference across its end provided the temperature remains constant.

------------------------------------------------------