Question

If eight resistor are connected in series to give equivalent resistance as 48ohms, then what is value each resistor

Answer 1

Given :

▪ Eight identical resistors are connected in series.

▪ Eq. resistance = 48Ω

To Find :

▪ Value of each resistor.

Solution :

↗ Eq. resistance of series connection is given by

✴ Req = R1 + R2 + ... + Rn

☞ Let resistance of each resistor be R.

ATQ, All are connected in series and equivalent resistance of connection is 48Ω.

↗ Req = 48Ω

↗ R1 = R2 = ... = R8 = R

→ Req = R1 + R2 + ... + R8

→ 48 = R + R + ... + R (8 times)

→ 48 = 8R

→ R = 48/8

→ R = 6Ω

፨ Value of each resistor = 6Ω

Answer 2

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$\bigstar$ CONCEPTS:-

(✷) when “n” no. of resistor connected in series and each resistor having resistance “R”, then equivalent Resistant is,

• Equivalent Resistant = R + R + ...... + R
• => Equivalent Resistant = “n × R”

(✷) when “n” no. of resistor connected in parallel and each having resistance “R”, then Equivalent Resistant is,

• {1/(Equivalent Resistant)} = 1/R + 1/R + .......+ 1/R
• => Equivalent Resistant = “R/n”

$\bigstar$ GIVEN:-

• Eight resistor connected in series to give equivalent Resistant = 48 ohms

$\bigstar$ SOLUTION:-

$\tt{\implies\:R_{1}\:+\:R_{2}\:+\:R_{3}\:+\:.\:.\:.\:.+\:R_{8}\:=\:48}$

$\tt{\implies\:R\:+\:R\:+\:R\:+\:R\:+\:R\:+\:R\:+\:R\:+\:R\:=\:48\:ohms}$

(☞ => 8 R = 48 ohms

(☞ => “R = 6 ohms”

✔️ Hence the value of each resistor is “6 Ohm”.

$\bigstar\:\underline{\boxed{\bf{\red{Required\: Answer\:=\:6\:Ohm}}}}$