Four resistors 100 Ω , 200 Ω, 300 Ω and 400 Ω are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square ?

Question

Four resistors 100 Ω , 200 Ω, 300 Ω and 400 Ω are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square ? (A) 210 Ω (B) 240 Ω (C) 300 Ω (D) 250 Ω

Tardigrade Admin · Accepted Answer

For maximum equivalent resistance across the diagonal of the square, the given resistors connected as

Resistance of

PQR

arm,

R_{1} = 300 + 200 = 500 Ω

Resistance of

PSR

arm,

R_{2} = 400 + 100 Ω = 500 Ω

The equivalent resistance between

P

and

R

.

\frac{1}{R _{eq}} = \frac{1}{R _{1}} + \frac{1}{R _{2}}

= \frac{1}{500} + \frac{1}{500} = \frac{1 + 1}{500}

∴ R_{eq} = \frac{500}{2}

= 250 Ω

Q. Four resistors $100 Ω, 200 Ω, 300 Ω$ and $400 Ω$ are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square ?

$210 Ω$

$240 Ω$

$300 Ω$

$250 Ω$

Q. Four resistors 100Ω,200Ω,300Ω and 400Ω are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square ?

210Ω

240Ω

300Ω

250Ω

Q. Four resistors $100 Ω, 200 Ω, 300 Ω$ and $400 Ω$ are connected to form four sides of a square. The resistors can be connected in any order. What is the maximum possible equivalent resistance across the diagonal of the square ?

$210 Ω$

$240 Ω$

$300 Ω$

$250 Ω$