Question

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

Answer 1

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

• 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.

Answer 2

${ \tt{ \huge{ \red{ \underline{ \underline{Question:-}}}}}}$

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

${ \tt{ \red{ \huge{ \underline{ \underline{Solution:-}}}}}}$

${ \rm{ \underline{ \underline{\purple{series \: combination}}}}}$

${ \dagger{ \sf{ \blue{ \: \: \: two \: resistors \: are \: said \: to \: be \: in \: series}}}} \\ \\ { \sf{ \blue{if \: only \: one \: of \: their \: end \: points \: is \: joined.}}}$

☛ If a third resistor is joined with the series combination of the two, then all three are said to be in series.

☛ Clearly, we can extend this definition to series combination of any number of resistors.

${ \star{\sf{ \green{ \: \: if \: there \: are \: n \: number \: of \: resistors}}}} \\ \\ { \sf{ \green{R1, \: R2 \:, ....... Rn \: connected \: in \: series}}}$

${ \pink{ \sf{the \: equivalent \: resistance \:}}}\\ \\ { \pink{ \sf (R \: eq \: ) = R1 \: + \: R2 \: + ..... + Rn}}$

${ \bold{ \purple{GIVEN:-}}}$

${ \blue{ \sf{equivalent \: resistance \: (R \: eq) = 48 \: Ω}}}$

${ \blue { \sf{ number \: of \: resistor = 8}}}$

${ \blue{ \sf{ type \: of \: combination = series}}}$

${ \star{ \pink{ \sf{ \: \: all \: the \: 8 \: resistors \: are \: equal \: .}}}}$

${ \sf{let \: the \: value \: of \: each \: resistor \: be \: R \: Ω}}$

${ \sf{ { \green{48 \: Ω = R + R + R + R + R + R + R + R}}}}$

${ \implies{ \sf{ \green{8 \: R \: = 48 \: Ω}}}}$

${ \implies{ \red{ \boxed{ \boxed{ \green{ \sf{ \: R \: \: = 6 \: Ω}}}}}}}$

${{ \sf{therefore}}} \\ \\ { \red{ \sf{the \: value \: of \: each \: resistor = 6 \: Ω}}}$