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Math Expert V
Joined: 02 Sep 2009
Posts: 55150
The amount of electrical current that flows through a wire is inversel  [#permalink]

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Difficulty:   15% (low)

Question Stats: 74% (01:17) correct 26% (01:27) wrong based on 120 sessions

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The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. If a wire currently carries 4 amperes of electrical current, but the resistance is then cut to one-third of its original value, how many of electrical current will flow through the wire?

A. 3/4 amperes
B. 4/3 amperes
C. 4 amperes
D. 8 amperes
E. 12 amperes

Kudos for a correct solution.

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Re: The amount of electrical current that flows through a wire is inversel  [#permalink]

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2
Let I1 be the initial current and R1 be the initial resistance.

I1 is inversely proportional to R1
i.e I1 = k/ R1 ; where k is some constant.

From the given data:
4 = k / R1
k = 4R1

Given R2 = R1/3
I2
= k/R2
= k/ R1/3
= 3k/ R1
= 3 * 4* R1/ R1
= 12 A

Answer E
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Re: The amount of electrical current that flows through a wire is inversel  [#permalink]

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The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. If a wire currently carries 4 amperes of electrical current, but the resistance is then cut to one-third of its original value, how many of electrical current will flow through the wire?

A. 3/4 amperes
B. 4/3 amperes
C. 4 amperes
D. 8 amperes
E. 12 amperes

Solution:

Given that, I∝1/R

I1=4 amps, I2=?
R2=(1/3)R1

Substitute the values in the equation (I1/I2)=(R2/R1) -> (4/I2) = (R1/3R1)

-> I2 = 12. ANS E.

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Re: The amount of electrical current that flows through a wire is inversel  [#permalink]

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Bunuel wrote:
The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. If a wire currently carries 4 amperes of electrical current, but the resistance is then cut to one-third of its original value, how many of electrical current will flow through the wire?

A. 3/4 amperes
B. 4/3 amperes
C. 4 amperes
D. 8 amperes
E. 12 amperes

Kudos for a correct solution.

Current flow = 4 ampere = 1/4 resistance
New Flow = 12 ampere = 1/12 resistance*

New resistance = 1/3 * 1/4 = 1/12

Answer E.
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The amount of electrical current that flows through a wire is inversel  [#permalink]

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Bunuel wrote:
The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. If a wire currently carries 4 amperes of electrical current, but the resistance is then cut to one-third of its original value, how many of electrical current will flow through the wire?

A. 3/4 amperes
B. 4/3 amperes
C. 4 amperes
D. 8 amperes
E. 12 amperes

Kudos for a correct solution.

Directly Proportional : The relation when due to increase in one variable, other variable needs to be increased is called a Directly Proportional Relationship e.g. Speed and Distance. "More Distance in same time require more speed and Vise versa"

Inversely Proportional : The relation when due to increase in one variable, other Variable needs to be Decreased is called a Inversely Proportional Relationship e.g. Speed and Time. "More Speed will cover a specific Distance in Less time and Vise versa"

Given: Current is INVERSELY Proportional to Resistance

i.e. Current = (1/Resistance)*Constant [Removal of Proportional sign always comes with a constant]

i.e. $$Current_1 / Current_2 = Resistance_2 / Resistance_1$$

If Initially Resistance = $$R_1$$
Then, $$R_2 = (1/3)*R_1$$
Current after reducing Resistance, $$C_2 = ?$$
Current Before reducing Resistance, $$C_1 = 4$$

$$4 / C_2 = (1/3)*R_1 / R_1$$

i.e. $$C_2 = 4*3 = 12$$ Amperes

Answer: Option
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Re: The amount of electrical current that flows through a wire is inversel  [#permalink]

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Bunuel wrote:
The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. If a wire currently carries 4 amperes of electrical current, but the resistance is then cut to one-third of its original value, how many of electrical current will flow through the wire?

A. 3/4 amperes
B. 4/3 amperes
C. 4 amperes
D. 8 amperes
E. 12 amperes

Kudos for a correct solution.

Current * resistance = K constant.

If resistance is dropped to 1/3rd then current must be tripled to maintain the product constant.

Hence Option E is correct.
Math Expert V
Joined: 02 Sep 2009
Posts: 55150
The amount of electrical current that flows through a wire is inversel  [#permalink]

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Bunuel wrote:
The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. If a wire currently carries 4 amperes of electrical current, but the resistance is then cut to one-third of its original value, how many of electrical current will flow through the wire?

A. 3/4 amperes
B. 4/3 amperes
C. 4 amperes
D. 8 amperes
E. 12 amperes

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

While you are not given precise amounts for the “before” or “after” resistance in the wire, you can pick numbers. Using 3 as the original resistance and 1 as the new resistance, you can see that the new electrical current will be 12 amperes:

$$C_1R_1=C_2R_2$$;

$$4*3=C_2*1$$;

$$C_2=12$$.

Answer: E.
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Re: The amount of electrical current that flows through a wire is inversel  [#permalink]

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4 = 1/R or R = 1/4
if resistance is cut to 1/3 of what it was, then the new resistance is 1/4 * 1/3 or 1/12

since we know that the amount of electrical current is indirectly proportional to resistance, then 1 : 1/12 = 12. Thus, E is the answer.
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GMAT 1: 620 Q46 V30 The amount of electrical current that flows through a wire is inversel  [#permalink]

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Voltage = Current * Resistance
Resistance drops to 1/3 of original value, therefore current will increase by 3 times.
4 * 3 = 12 A
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Re: The amount of electrical current that flows through a wire is inversel  [#permalink]

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$$c=\frac{k}{r}$$
$$4=\frac{k}{r}$$
$$k=4r$$

After cutting resistance

$$c=\frac{k}{\frac{r}{3}}$$
$$c=\frac{3k}{r}$$
$$c=\frac{3*4r}{r}$$
$$c=12$$
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Re: The amount of electrical current that flows through a wire is inversel  [#permalink]

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Bunuel wrote:
The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. If a wire currently carries 4 amperes of electrical current, but the resistance is then cut to one-third of its original value, how many of electrical current will flow through the wire?

A. 3/4 amperes
B. 4/3 amperes
C. 4 amperes
D. 8 amperes
E. 12 amperes

Kudos for a correct solution.

For a conceptual discussion of inverse variation, check this link:
https://www.veritasprep.com/blog/2013/0 ... inversely/
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Re: The amount of electrical current that flows through a wire is inversel  [#permalink]

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_________________ Re: The amount of electrical current that flows through a wire is inversel   [#permalink] 16 May 2019, 21:24
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