Posted by David on Saturday, November 17, 2012 at 3:05am.
3. Ohm’s law states that the current flowing in a circuit varies directly as the applied voltage and inversely as the resistance. In an experiment, the resistance was increased by triple the percentage by which the voltage was increased. A student calculated the percent change in current to be 15%. Is the student correct?
• If yes, determine the percent change in voltage and resistance to three significant digits.
• If no, explain why and give an example of nonzero percent changes in V and R that would result in a 15% increase in I.

Maths  Henry, Monday, November 19, 2012 at 8:26pm
I1 = V/R.
Let V increase by 10%; then increase R
by 3 times as much(30%).
I2 = (V+0.1V)/(R+0.3R).
I2 = 1.1V/1.3R = 0.85V/R.
I2/I1 = (0.85V/R) / (V/R) = 0.85 = 85%.
%Change = 85%100% = 15% = 15% Decrease
However, this value is valid for a 10%
increase in V only.
If V is increased by 20% and R increased by 3 times as much(60%),the
results is completely different:
I = 1.2V/1.6R = 0.75V/R. This is the
same as decreasing V by a factor of 0.75
while holding R constant. In the first
example, V was decreased by a factor of
0.85. Therefore, we cannot consider the student's calculation as being correct
unless the % increase in V was given.
I1 = V/R.
I2 = (V+3p*V)/(R+p*R).
I2 = V(1+3p)/R(1+p).
I2/I1 = (V(1+3p)/R(1+p))/(V/R).
The Vs and Rs cancel:
I2/I1 = (1+3p)/(1+p) = 1.15
(1+3p)/(1+p) = 1.15
Multiply both sides by (1+p):
1+3p = 1.15+1.15p
1.85p = 0.15
P = 0.081 = 8.1 % Increase in R.
3p = 3*.081 = 0.243 = 24.3% Increase in V.
Check:
I2 =(V+0.243V)/(R+0.081R)
I2 = 1.243V/1.081R = 1.15V/R.
I2/I1 = (1.15V/R) / (V/R) = 1.15 = 115%
%Change=115  !00% = 15% = 15% Increase.
;
Answer This Question
Related Questions
 physics  resistors of 30 ohms and 60 ohms are connected in parallel and joined...
 physics  resistors of 30 ohms and 60 ohms are connected in parallel and joined...
 physcial science  Which of the following statements about Ohm’s Law is true? A...
 physics.  resistors of 30 ohms and 60 ohms are connected in parallel and joined...
 Intermediate Algebra  The amount of current flowing into an electrical circuit ...
 Physics  For voltage variation with length, in using a slide meter, the wire ...
 Algebra  The heat generated by a stove element varies directly as the square of...
 physics  The current a series circuit in 5A when an additional resistance of 2 ...
 Calculus 1  According to Ohm's law, the voltage V, current I, and resistance R ...
 physics  the table below shows the values of the resistance, capcitive ...
More Related Questions