The amount of electrical current that flows through a wire is inversel

Question

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.

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

askhere · Answer

Let  I 1 be the initial current and  R 1 be the initial resistance.

I1 is inversely proportional to R1
i.e  I 1 = k/  R 1 ; where k is some constant.

From the given data:
4 = k /  R 1
k = 4 R 1

Given  R 2 =  R 1/3
 I 2 
= k/ R 2
= k/  R 1/3
= 3k/  R 1
= 3 * 4*  R 1/  R 1
= 12 A

Answer  E

balamoon · Answer

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.

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.

Thanks

Kudos Please

reto · Answer

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

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

Answer E.

GMATinsight · Answer

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

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  E

vishwaprakash · Answer

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.

Bunuel · Answer

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.

mvictor · Answer

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.

Manick9 · Answer

Voltage = Current * Resistance
Resistance drops to 1/3 of original value, therefore current will increase by 3 times.
4 * 3 = 12 A

Mahmud6 · Answer

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

KarishmaB · Answer

For a conceptual discussion of inverse variation, check this link: https://youtu.be/AT86tjxJ-f0

bumpbot · Answer

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The amount of electrical current that flows through a wire is inversel

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