Question

Four resistors 1Ω, 7 Ω, RΩ and 3Ω, are connected in series in a circuit. If the resultant resistance in the circuit is 15 Ω then the value of R is ____​

Answer 1

Given :

Four resistors are connected in series,

• R₁ = 1Ω
• R₂ = 7Ω
• R₃ = RΩ
• R₄ = 3Ω

The resultant resistance in the circuit = 15Ω

To find :

The value of R

Solution :

According to the law of combination of resistance,

The combined resistance of any number of resistance connected in series is equal to the sum of the individual resistances .i.e.,

$\boxed{\bf R_{eq} = R_1 + R_2 + R_3 + R_4}$

by substituting all the given values in the formula,

$\leadsto \sf R_{eq} = R_1 + R_2 + R_3 + R_4$

$\leadsto \sf 15 = 1 + 7 + R + 3$

$\leadsto \sf 15 = 11+ R$

$\leadsto \sf R = 15 - 11$

$\leadsto \underline {\boxed {\sf R = 4 \: \Omega}}$

thus, the value of R is 4 Ω.

Remember !

The SI unit of resistance is ohms (Ω).

Answer 2

Answer:

ǫᴜᴇsᴛɪᴏɴ

Four resistors 1Ω, 7 Ω, RΩ and 3Ω, are connected in series in a circuit. If the resultant resistance in the circuit is 15 Ω then the value of R is ____

ɢɪᴠᴇɴ

• R₁ = 1Ω
• R₂ = 7Ω
• R₃ = RΩ
• R₄ = 3Ω

the resultant resistance in the circuit is 15 Ω.

ᴛᴏ ғɪɴᴅ

value of RΩ

sᴏʟᴜᴛɪᴏɴ

❐ The total resistance of the series system is just the total of individual resistors.

✧The following relation gives the total resistance of a series circuit:

$\bold {➙R_{eq} = R_{1} + R_{2} + R_{3} + .... + R_{n}}$

substitute the values in the above formula:--

$\bold {➙ \: 15= 1 + 7 + R+ 3} \\ \\ ➙15 = 11 + R \\ \\ ➙R = 15 - 11 \\ \\ ➙ \bold \purple{R = 4Ω}$

so the value of unknown Resistor is 4 Ω.

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More information!!

⚡ohm's law - the current passing through metallic element is directly proportional to the potential difference across ends, provided the temperature remains constant.

⚡Resistance- it is the property of a conductor by which it obstructs the flow of current through it.

• R= V/I

⚡higher the resistance.. lower is the current

⚡good conductor have low resistance.

⚡unit of Resistance is ohm.

• 1 ohm = 1 volt /1 ampere

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