20 Physics -- DC Circuits

You are given 2 wires each of resistance R . What is the ratio to minimum resistance that can be obtained from these wires .

1 Answers

If we have two wires, each with a resistance of R, the minimum resistance that can be obtained by combining them in a specific way is R/4.

To achieve this minimum resistance, the wires need to be connected in parallel. When two resistors are connected in parallel, the total resistance is given by the formula:

1/R_total = 1/R1 + 1/R2

In this case, substituting R for both R1 and R2, we get:

1/R_total = 1/R + 1/R = 2/R

Taking the reciprocal of both sides:

R_total = R/2

Therefore, the ratio of the minimum resistance (R/4) to the resistance of each individual wire (R) is:

(R/4) / R = 1/4

What is the smallest number of 1Ω resistors needed such that when arranged in a certain arrangement involving only series and parallel connections, that the equivalent resistance is (7/6)Ω?

A storage battery of emf 8V and internal resistance 0.5ohm is discharged through a parallel combination of to resistor each of resistance 15 ohm. What is the terminal voltage of the battery? [3]a)...

Emf =8V,

Internal resistance r=0.5Ω
R1 = R2 = 15 Ω

Equivalent capacitance of R1 and R2 is

R= 7.5 Ω

now,

emf = I (R+r)
8 = I (7.5+0.5)

8 = I 8
I = 1A

Now,

E= IR+ Ir
E = V + Ir
8 = V + 1x0.5

V= 7.5 volt

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