Question

Five resistance, each of 5 Ω, are connected as shown in figure. Find the equivalent resistance between points (1) A and B, (2) A and C.(a) (1) 7.5 Ω (2)2.25 Ω(b) (1) 5 Ω (2) 2.50 Ω(c) (1) 2.5 Ω (2) 3.13 Ω(d) (1) 3 Ω (2) 2.50 Ω

Answer 1

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Answer 2

$\huge \bold{RESISTANCE}$

Resistance is the obstruction offered in the path of the current.

◼When resistors are connected in series the total resistance is equal to

$\boxed{R_s = R_1 + R_2 + n \: resistors }$

◼When resistors are connected in parallel the total resistance is equal to

$\boxed{\dfrac{1}{R_s} = \dfrac{1}{R_1}+\dfrac{1}{R_2} + n resistors }$

$\huge \bold{IN \: THE \: FIGURE}$

$\bold{RESISTANCE \: BETWEEN \: A \: AND \: B \: WILL \: BE}$

Let the point from which the wire in divided into three parallel parts be$\bold{ P}$ and the point where the unite be $\bold{ Q}$ and the resistor in middle be $\bold{R_p}$

So net resistance between P and Q is

$\mathsf{R_{s1} = 5 + 5 }$

$\boxed{R_{s1} = 10 \: ohm }$

So net resistance between P ,C and Q is

$\mathsf{R_{s2} = 5 + 5 }$

$\boxed{R_{s2} = 10 \: ohm }$

Since, $\bold{R_p , R_{s1} \: and R_{s2} \: are \: in \: parallel }$

So, total resistance R will be

$\boxed{\dfrac{1}{R} = \dfrac{1}{R_{s1}}+ \dfrac{1}{R_p}+\dfrac{1}{R_{s2}}}$

$\mathsf{\dfrac{1}{R} = \dfrac{1}{10}+ \dfrac{1}{5}+\dfrac{1}{10}}$

$\mathsf{\dfrac{1}{R} = \dfrac{1+1+2}{10}}$

$\mathsf{\dfrac{1}{R} = \dfrac{4}{10}}$

$\mathsf{R = \dfrac{10}{4}}$

$\huge \boxed{\mathsf{R = 2.5 \: ohm}}$

$\bold{RESISTANCE \: BETWEEN \: A \: AND \: C \: WILL \: BE}$

The resistor between A, B and C are in series,

So net resistance between P and Q is

$\mathsf{R_{s3} = 5 + 5 }$

$\boxed{R_{s3} = 10 \: ohm }$

$\bold{Resistor R_{s3} \: and \: R_p \: are \: in \: parallel}$

So, total resistance$R_2$ will be

$\boxed{\dfrac{1}{R_2} = \dfrac{1}{R_{s3}}+ \dfrac{1}{R_p}}$

$\mathsf{\dfrac{1}{R_2} = \dfrac{1}{10}+ \dfrac{1}{5}}$

$\mathsf{\dfrac{1}{R_2} = \dfrac{1 + 2}{10}}$

$\mathsf{\dfrac{1}{R_2} = \dfrac{3}{10}}$

$\mathsf{R_2 = \dfrac{10}{3}}$

$\huge \boxed{\mathsf{R = 3.33 \: ohm}}$