If eight equal resistors are connected in series to give equivalent re

1.	If eight equal resistors are connected in series to give equivalent resistance as 48Ω, then what is the value each resistor?
Answer» $\large\bf\underline{Given:-}$ 8 RESISTORS are connected in series and give equivalent resistance 48Ω. $\large\bf\underline {To \: find:-}$ Value of each resistor $\huge\bf\underline{Solution:-}$ we know that, $\tt \large \: R_P = R_1 + R_2 + R_3.......R_8$ $\bullet \: \tt \: R_P = 48\Omega$ It is given that 8 resistors are equal $\tt = R_1 + R_2 + R_4 + R_5 + R_6 + R_7+ R_8 =8 R$ $\tt \large \: R_P = R_1 + R_2 + R_3.......R_8 \\ \\ \tt \dashrightarrow \: 48 = 8R \\ \\ \tt \dashrightarrow \:R = \cancel\dfrac{48}{8} \\ \\ \bf \dashrightarrow \:R = 6 \Omega$ Hence, ≫ Value of each resistor = 6 ohm. Verification:- Rp = R1 + R2 + R3 + R4 + R5 + R6 + R7 + R8 48 = 6 + 6+ 6 + 6 + 6 + 6+ 6 + 6 48 = 48 LHS = RHS hence value of R = 6ohm is correct.

If eight equal resistors are connected in series to give equivalent resistance as 48Ω, then what is the value each resistor?

Answer»

$\large\bf\underline{Given:-}$

8 RESISTORS are connected in series and give equivalent resistance 48Ω.

$\large\bf\underline {To \: find:-}$

Value of each resistor

$\huge\bf\underline{Solution:-}$

we know that,

$\tt \large \: R_P = R_1 + R_2 + R_3.......R_8$

$\bullet \: \tt \: R_P = 48\Omega$

It is given that 8 resistors are equal

$\tt = R_1 + R_2 + R_4 + R_5 + R_6 + R_7+ R_8 =8 R$

$\tt \large \: R_P = R_1 + R_2 + R_3.......R_8 \\ \\ \tt \dashrightarrow \: 48 = 8R \\ \\ \tt \dashrightarrow \:R = \cancel\dfrac{48}{8} \\ \\ \bf \dashrightarrow \:R = 6 \Omega$

Hence,

≫ Value of each resistor = 6 ohm.

Verification:-

Rp = R1 + R2 + R3 + R4 + R5 + R6 + R7 + R8

48 = 6 + 6+ 6 + 6 + 6 + 6+ 6 + 6

48 = 48

LHS = RHS

hence value of R = 6ohm is correct.

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