Question

Calculate equivalent resistance in the following between points P and Q​.

Answer 1

$\sf{(i) \: We \: are \: given \: a \: figure \: of \: Series \: Circuit. }$

$\sf{Here \: Resistances \: are ,}$

$\sf• \: R_{1} =3 Ω$

$\sf• \: R_{2} =3Ω$

$\sf• \: R_{3} =3Ω$

$\sf{We \: know \: the \: formula \: of \: the \: Equivalent \: Resistance \: for \: Series \: Circuit, }$

$\bf \red {\bigstar {\: R_{s} = R _{1} + R _{2} + R_{3}+...+ R_{n}}}$

$\sf ⇒ R_{s} =(3 + 3 + 3)Ω$

$\sf \therefore R_{s} =9Ω$

$\sf \pink{ \boxed{Answer : 9 Ω.}}$

$\sf{(ii) \: We \: are \: given \: a \: figure \: of \: Parallel \: Circuit. }$

$\sf{Here \: Resistances \: are ,}$

$\sf• \: R_{1} =3 Ω$

$\sf• \: R_{2} =3 Ω$

$\sf• \: R_{3} =3 Ω$

$\sf{We \: know \: the \: formula \: of \: the \: Equivalent \: Resistance \: for \: Parallel \: Circuit, }$

$\bf \red {\bigstar {\: \frac{1}{R_{p}} = \frac{1}{R _{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}+...+\frac{1}{R_{n}} }}$

$\sf⇒ \frac{1}{ R_{p} } = \frac{1}{3} + \frac{1}{3} + \frac{1}{3}$

$\sf⇒ \frac{1}{ R_{p} } = \frac{1 + 1 + 1}{3}$

$\sf⇒ \frac{1}{ R_{p} } = \frac{3}{3}$

$\sf⇒ \frac{1}{ R_{p} } = 1$

$\sf \therefore R_{p} = 1Ω$

$\sf \pink{ \boxed{Answer : 1 Ω.}}$

Answer 2

$\sf{(i) \: We \: are \: given \: a \: figure \: of \: Series \: Circuit. }$

$\sf{Here \: Resistances \: are ,}$

$\sf• \: R_{1} =3 Ω$

$\sf• \: R_{2} =3Ω$

$\sf• \: R_{3} =3Ω$

$\sf{We \: know \: the \: formula \: of \: the \: Equivalent \: Resistance \: for \: Series \: Circuit, }$

$\bf \red {\bigstar {\: R_{s} = R _{1} + R _{2} + R_{3}+...+ R_{n}}}$

$\sf ⇒ R_{s} =(3 + 3 + 3)Ω$

$\sf \therefore R_{s} =9Ω$

$\sf \pink{ \boxed{Answer : 9 Ω.}}$

$\sf{(ii) \: We \: are \: given \: a \: figure \: of \: Parallel \: Circuit. }$

$\sf{Here \: Resistances \: are ,}$

$\sf• \: R_{1} =3 Ω$

$\sf• \: R_{2} =3 Ω$

$\sf• \: R_{3} =3 Ω$

$\sf{We \: know \: the \: formula \: of \: the \: Equivalent \: Resistance \: for \: Parallel \: Circuit, }$