Ask question

Ask question

All categories

3 years ago

7

The electronics supply company where you work has two different resistors, R1 and R2, in its inventory, and you must measure the

values of their resistances. Unfortunately, stock is low, and all you have are R1 and R2 in parallel and in series - and you can't separate these two resistor combinations. You separately connect each resistor network to a battery with emf 39.0 V and negligible internal resistance and measure the power P supplied by the battery in both cases. For the series combination, P = 48.0 W; for the parallel combination, P = 256 W. You are told that R1>R2.
Calculate R1

1 answer:

elixir [45]3 years ago

3 0

Answer:

R₁ = 23.77 ohms and R₂ = 7.92 ohms

Explanation:

When connected in series, the equivalence resistance, R(eq) is given as

R(eq) = (R₁ + R₂)

When connected in parallel, the equivalence resistance, R(eq) is given as

[1/R(eq)] = [(1/R₁) + (1/R₂)]

R(eq) = (R₁R₂)/(R₁ + R₂)

The parallel and series combination are connected to a battery of emf 39.0 V with negligible internal resistance. And the power supplied is measured.

But power supplied is given as

P = IV = (V/R) V = (V²/R)

When connected in series, the power supplied is given as

P = 48.0 W,

V = 39.0 V,

R = R(eq) = (R₁ + R₂)

48 = (39²/R)

R = (39²/48)

R = 31.6875 ohms

R = (R₁ + R₂) = 31.6875

(R₁ + R₂) = 31.6875 (eqn 1)

When connected in series, the power supplied is given as

P = 256.0 W,

V = 39.0 V,

R = R(eq) = (R₁R₂)/(R₁ + R₂)

256 = (39²/R)

R = (39²/256)

R = 5.9414 ohms

R = R(eq) = (R₁R₂)/(R₁ + R₂) = 5.9414

(R₁R₂)/(R₁ + R₂) = 5.9414

But, recall eqn 1

(R₁ + R₂) = 31.6875

(R₁R₂)/(R₁ + R₂) = 5.9414

Substituting for (R₁ + R₂)

(R₁R₂)/(R₁ + R₂) = (R₁R₂)/31.6875 = 5.9414

(R₁R₂) = 31.6875 × 5.9414 = 188.2683

R₁ = (188.2683/R₂)

(R₁ + R₂) = 31.6875

Substituting for R₁

(188.2683/R₂) + R₂ = 31.6875

multiply through by R₂

188.2683 + R₂² = 31.6875R₂

R₂² - 31.6875R₂ + 188.2683 = 0

Solving the quadratic equation

R₂ = 23.77 ohms or 7.92 ohms

If R₂ = 23.77 ohms, R₁ = 7.92 ohms

If R₂ = 7.92 ohms, R₁ = 23.77 ohms

Since the question explains that R₁ > R₂

R₁ = 23.77 ohms and R₂ = 7.92 ohms

Hope this Helps!!!

You might be interested in

Charge q is 1 unit of distance away from the source charge S. Charge p is two times further away. The force exerted between S an

insens350 [35]

Answer : The correct option is, (d) 4 times

Solution :

According to the Coulomb's law, the electrostatic force of attraction or repulsion between two charges is directly proportional to the product of the charges and is inversely proportional to the square of the distance between the the charges.

Formula used :

$F=k_e\frac{q_1q_2}{r^2}$

where,

F = electrostatic force of attraction or repulsion

$k_e$ = Coulomb's constant

$q_1$ and $q_2$ are the charges

r = distance between two charges

First we have to calculate the force exerted between S and q when the distance between the charge is 1 unit and let us assumed that the charge be 'q'

$F_{sq}=k_e\frac{qq}{1^2}=k_e\times q^2$ ..........(1)

Now we have to calculate the force exerted between S and p when the distance between the charge is 2 unit at the same charge.

$F_{sp}=k_e\frac{qq}{2^2}=k_e\frac{q^2}{4}$ ...........(2)

Equation equation 1 and 2, we get

$\frac{F_{sq}}{F_{sp}}=\frac{1}{4}$

$F_{sq}=4\times F_{sp}$

Therefore, the force exerted between S and q is 4 times the force exerted between S and p.

5 0

3 years ago

Read 2 more answers

2. Ms. Evelyn lined up her students at recess on the soccer field. She told each student to kick a soccer ball as hard as they c

mash [69]

Answer

A. Yes, because they did several tests with the soccer balls and recorded their observations. B. Yes, because every student kicked

Explanation:

5 0

2 years ago

An airplane flies in a horizontal circle of radius 500 m at a speed of 150 m/s. If the radius were changed to 1000 m, but the sp

laila [671]

Answer:

The centripetal acceleration changed by a factor of 0.5

Explanation:

Given;

first radius of the horizontal circle, r₁ = 500 m

speed of the airplane, v = 150 m/s

second radius of the airplane, r₂ = 1000 m

Centripetal acceleration is given as;

$a = \frac{v^2}{r}$

At constant speed, we will have;

$v^2 =ar\\\\v = \sqrt{ar}\\\\at \ constant\ v;\\\sqrt{a_1r_1} = \sqrt{a_2r_2}\\\\a_1r_1 = a_2r_2\\\\a_2 = \frac{a_1r_1}{r_2} \\\\a_2 = \frac{a_1*500}{1000}\\\\a_2 = \frac{a_1}{2} \\\\a_2 = \frac{1}{2} a_1$

a₂ = 0.5a₁

Therefore, the centripetal acceleration changed by a factor of 0.5

7 0

3 years ago

What rapid changes to earths surface are caused by shifting plates

PtichkaEL [24]

I am not sure if this is the answer you are looking for but a earthquake occurs when the plates shift.
Hope this helped.

4 0

2 years ago

Help with this question please.

mr Goodwill [35]

There are 4 hydrogens on the right side $(2\mathrm H_2=4\mathrm H)$ , and 2 hydrogens on the left per molecule of $\mathrm H_2$ . To get the same number of hydrogens on both sides, the coefficient should be 2.

(Then the number of oxygens will be consistent, since $2\mathrm H_2\mathrm O$ contributes 2 oxygens, and so does $\mathrm O_2$ .)

5 0

3 years ago