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In FIGURE EX28.31, what is the value of the potential at points aandb?

Short Answer

Expert verified

The potential at points aandbareVa=5VandVb=-2V

Step by step solution

01

Given information and formula used 

Given :

Theory used :

Kirchhoff's loop rule states that the sum of all the electric potential differences around a loop is zero. It is also sometimes called Kirchhoff's voltage law or Kirchhoff's second law.

02

Finding the value of current

The ground wire has no effect on the circuit's behavior, but it does provide a location on the circuit with zero potential, which is the same as the potential of the earth.

As a result, the potential zero is at point 'c'.

Assume we proceed around a loop, measuring potential differences among circuit parts along the way, and when we get back to the starting point, the algebraic sum of these differences is zero.

ฮฃV=0

Let's create a clockwise loop and apply equation (28.2) to it, with the voltage across the resistors role="math" localid="1649354732313" R1=1ฮฉandR2=4ฮฉbeing negative because the current is flowing in the same direction.

The emf role="math" localid="1649354742862" ฮต1=15Vis positive because the current flows from the negative to the positive terminal in the battery, whereas the emf ฮต2=5Vis negative because the current flows from the positive to the negative terminal.

ฮฃV=0โ‡’ฮต1+โˆ†Vโ‚+โˆ†Vโ‚‚-ฮต2=0โ‡’ฮต1+IR1+IR2-ฮต2=0โ‡’I=ฮต1-ฮต2R1+R2

Put the values to get :

I=ฮต1-ฮต2R1+R2=15V-5V1ฮฉ+4ฮฉ=2A

03

Finding value of the potential at points a and b

The current is positive, indicating that it is moving in a clockwise direction. Because the current should move from the greater potential to the lower potential while moving clockwise, it passes through point 'c' before point 'a', resulting in a negative differential between the two places.

Va-Vc=5Volts

We may getVa=Vc+5V=0+5V=5Vby putting the value of Vc

To calculate the voltage across the resistance, we use Ohm's law.

โˆ†V1=IR1=(2A)(1ฮฉ)=2V

Because the current goes from the greater potential to the lower potential when it passes through point 'b' before point 'c', the difference between the two points is positive.

role="math" localid="1649355013833" Vb-Vc=-2V

By plugging in the value of Vcby zero :

Vb=Vc-2V=0-2V=-2V

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