A loop circuit has a resistance of R1 and a current of 2.2 A. The current is reduced to 1.7 A when an additional 3 Ω resistor is added in series with R1. What is the value of R1? Assume the internal resistance of the source of emf is zero.
Got 12.75 however that answer is incorrect.
The correct answer was actually 10.2
2.2R=1.7(3+R)
2.2R=5.1+1.7R
.5R=5.1
R=10.2
To find the value of R1, we can use Ohm's Law and the concept of series resistance in a loop circuit.
1. First, let's find the resistance of the loop circuit without the additional resistor:
According to Ohm's Law, V = I * R, where V is the voltage across the resistor, I is the current flowing through it, and R is the resistance.
Since the current is 2.2 A, and assuming the voltage across R1 is V1, we have V1 = 2.2 * R1.
2. Next, let's consider the circuit with the additional 3 Ω resistor:
When the additional resistor is added in series, the total resistance of the circuit becomes R_total = R1 + 3 Ω.
According to Ohm's Law, the current flowing through the circuit is now 1.7 A, and the voltage across R_total is V_total.
Thus, V_total = 1.7 * (R1 + 3 Ω).
3. Since the internal resistance of the source of emf is assumed to be zero, the total voltage across the circuit should remain constant.
Therefore, we can equate the voltage across R1 in the first circuit (V1) to the voltage across R_total in the second circuit (V_total):
V1 = V_total.
4. Substituting the previously found expressions for V1 and V_total, we have:
2.2 * R1 = 1.7 * (R1 + 3 Ω).
5. Now, we can solve the equation for R1:
Multiply 1.7 by R1 + 3 Ω:
2.2 * R1 = 1.7 * R1 + 1.7 * 3 Ω.
Simplify the equation:
2.2 * R1 = 1.7 * R1 + 5.1 Ω.
Subtract 1.7 * R1 from both sides:
0.5 * R1 = 5.1 Ω.
Divide both sides by 0.5:
R1 = 10.2 Ω.
Therefore, the value of R1 is 10.2 Ω.
V2 = I*R2 = 1.7 * 3 = 5.1 Volts.
R1 = Change in voltage/Change in I = -5.1/(1.7-2.2) = 10.2 Ohms.
well, it is right. Recheck to see you typed the problem right. I would be concerned with significant digits on this one, you gave the answer to four digits,I think I would have assumed the 3 ohm was 3.0, and take the answer to two digits.
Here is almost identical quiz problem: http://myspace.upike.edu/rarts/public_html/courses/physics/Physics/Physics2/hw/2015/HW_4%20-%20Current,%20Resistance,%20and%20Basic%20Circuits-preview3.pdf
on page 2, continued on 3.
2.2*R1=1.7(3+R1)
2.2R1-1.7R1=5.1
.4R1=5.1
R1=...