Figure shows a circuit of four resistors that are connected to a larger circuit. The graph below the circuit shows the electric potential V(x) as a function of position xalong the lower branch of the circuit, through resistor 4; the potential VAis 12.0 V. The graph above the circuit shows the electric potential V(x) versus position x along the upper branch of the circuit, through resistors 1, 2, and 3; the potential differences areΔVB2.00 V andΔVC5.00 V. Resistor 3 has a resistance of 200 Ω. What is the resistance of (a) Resistor 1 and (b) Resistor 2?

Short Answer

Expert verified
  1. The resistance of Resistor 1 isr1=80
  2. The resistance of Resistor 2 isr2=200

Step by step solution

01

Given

  1. PotentialVA=12V
  2. Potential differenceΔVB=2
  3. Potential differencerole="math" ΔVC=5
  4. Resistancer3=200
02

Determining the concept

Using the property of parallel circuit, find the voltagedrop across resistor 3. Inserting it in the Ohm’s law, find the current in the circuit.Also, apply Ohm’s law to resistor 1 and resistor 2 and can find the values of their resistances.

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

Formulae are as follow:

I=VR

Where, I is current, V is voltage, R is resistance.

03

(a) determining the resistance of resistor 1

The resistance of resistor 1:

Since, the resistances in upper and lower branch are parallel, the voltage drop across both branches is equal.

So, the voltage drop across the upper branch is 12 V.

Hence, the voltage drop across the resistor 3 is 5V and the current in the circuit is given by,

i=ΔVr3i=5V200Ωi=25mA

Then the resistance of resistor 1 will be,

i=ΔVr1r1=2V25mAr1=80

Hence, the resistance of Resistor 1 isr1=80Ω

04

(b) determining the resistance of resistor 2

The resistance of resistor 2 :

From the graph, we can see that the resistor 2 has the same voltage drop as the resistor 3 and is given by,

ΔV=5V

Its resistance is then given by,

i=ΔVr2r2=ΔVir2=5V25mAr2=200

Hence, the resistance of Resistor 2 isr2=200Ω

Therefore, by using ohms law the resistance of the resistors can be determined.

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Most popular questions from this chapter

In Fig. 27-33,Battery1 has emf V and internal resistancer1=0.016and battery 2has emf V and internal resistancer2=0.012.The batteries are connected in series with an external resistance R.

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