1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
strojnjashka [21]
2 years ago
14

Two resistances, R1 and R2, are connected in series across a 9-V battery. The current increases by 0.450 A when R2 is removed, l

eaving R1 connected across the battery. However, the current increases by just 0.225 A when R1 is removed, leaving R2 connected across the battery. a) Find R1 b) Find R2
Physics
1 answer:
Rina8888 [55]2 years ago
5 0

Answer:

a. R1 = 0.162 Ω

b. R2 = 0.340 Ω

Explanation:

Since the resistors R1 and R2 are connected in series, the current flowing through them when the 9 V battery is applied is 9/R1 + R2.

When the current increases by 0.450 A wen only R1 is in the circuit, the current is

9/R1 + R2 + 0.450 A = 9/R1       (1)

When the current increases by 0.225 A when only R2 is in the circuit, the current is

9/R1 + R2 + 0.225 A = 9/R2       (2)

equation (1) - (2) equals

9(1/R1 - 1/R2) = 0.450 A - 0.225

9(1/R1 - 1/R2) = 0.125

(1/R1 - 1/R2) = 0.125 A/9 = 0.0138

1/R1 = 0.0138 + 1/R2

R1 = R2/(1 + 0.0138R2)     (3)

From (1)

9/R1 - 9/R1 + R2 = 0.450 A

9R2/[R1(R1 + R2)] = 0.450 A

R2/[R1(R1 + R2)] = 0.450 A/9 = 0.5

R2/[R1(R1 + R2)] = 0.5    (4)

From (3) R2/R1 = (1 + 0.0138R2) and from (4) R2/R1 = 0.5(R1 + R2). So,

(1 + 0.0138R2) = 0.5(R1 + R2)

0.5R1 + 0.5R2 = 1 + 0.0138R2

0.5R1 = 1 + 0.0138R2 - 0.5R2

0.5R1 = 1 - 0.4862R2        (5)

Substituting (3) into (5) we have

0.5R2/(1 + 0.0138R2) = 1 - 0.4862R2

R2 = (1 + 0.0138R2)(1 - 0.4862R2)

R2 = 1 - 0.4724R2 - 0.0067R2²

Collecting like terms, we have

0.0067R2² + 0.4724R2 + R2 - 1 = 0

0.0067R2² + 1.4724R2 - 1 = 0

Using the quadratic formula,

R_{2} = \frac{-1.4724 +/-\sqrt{(1.4724)^{2} - 4 X 0.0067 X -1} }{2 X 0.0067}  \\= \frac{-1.4724 +/-\sqrt{2.1680 + 0.0268} }{0.0268}\\= \frac{-1.4724 +/-\sqrt{2.1948} }{0.0268}\\= \frac{-1.4724 +/- 1.4815 }{0.0268}\\= \frac{-1.4724 + 1.4815 }{0.0268} or \frac{-1.4724 - 1.4815 }{0.0268}\\= \frac{0.0091 }{0.0268} or \frac{-2.9539}{0.0268}\\= 0.340 or -110.22

We choose the positive answer.

So R2 = 0.340 Ω

From (5)

R1 = 0.5 - 0.9931R2

   = 0.5 - 0.9931 × 0.340

   = 0.5 - 0.338

   = 0.162 Ω

a. R1 = 0.162 Ω

b. R2 = 0.340 Ω

You might be interested in
Who actually asked Abraham to sacrifice his son?
pochemuha

I think god did ??? I searched it up okay

7 0
2 years ago
Read 2 more answers
A box weighs 100N and its base area of 2 m2. What pressure does it exert on the ground?
kotegsom [21]

Answer:

P = F/S = 100/2 =50 (N/m2)

5 0
2 years ago
What are the unit for acceleration
Flura [38]
<h3>Answer</h3>

m/s^2 (meter per sec square)

Explanation:

acc = change in velocity/time

= distance/time

----------------

time

= m/s

------

s

=m/s^2

7 0
3 years ago
What variable is the dependent variable?<br><br> A. Time<br> B. Temperature
melomori [17]

Answer:

the answer is b temperature

6 0
3 years ago
Read 2 more answers
A cat jumps off a piano that is 1.3m high. The initial velocity of the cat is 3m/s at an angle of 37degrees above the horizontal
SpyIntel [72]

Answer:

x=1.75m

Explanation:

From the exercise we have that

y_{o}=1.3m\\v_{o}=3m/s, \beta  =37\\

<em><u>To find how far from the edge of the piano does the cat strike the floor, we need to calculate its time first </u></em>

y=y_{o}+v_{oy}t+\frac{1}{2}gt^{2}

At the end of the motion y=0m

0=1.3+3sin(37)t-\frac{1}{2}(9.8)t^{2}

Solving for t

t=-0.36 s or t=0.73s

Since the <u>time</u> can't be negative the answer is t=0.73

Knowing that we can calculate how far does the cat strike the floor

x=v_{ox}t=3cos(37)(0.73)=1.75m

6 0
3 years ago
Other questions:
  • Which of the following does NOT describe the conversion of potential to kinetic energy? Question 12 options:
    13·1 answer
  • Newton's law of universal gravitation can be applied to
    5·2 answers
  • Terry is convinced that heating peanut butter will increase its mass so that it covers more bread. Is he correct?
    10·1 answer
  • Question 1 of 10
    14·1 answer
  • A 34n force is applied to a 213kg mass how much does the mass accelerate
    11·1 answer
  • What’s the voltage of a battery in a circuit with resistance of 3 ohms and current of 5 amps?
    10·1 answer
  • Which statement about the water cycle is correct.
    6·1 answer
  • A moving car has 2000 J of kinetic energy. If the speed doubles, how much kinetic energy would it have?
    13·1 answer
  • Fnet = fa + ff or fnet = fa - ff
    5·1 answer
  • 5. Find the velocity of a train that traveled 75 km in 35 minutes. (answer
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!