Solving 2 Questions on Circuit Analysis: PD Across 3 Ohm & EMF of Batteries

In summary: You need to take the equivalent of the internal resistor and this is done by taking the reciprocal of the sum of the reciprocals of all the resistors. So for three resistors like this it is one third.In summary, the first question involves a wheatstone bridge and the potential difference across the 3 ohm resistor is zero due to the relationship between the other resistors. The second question addresses the need to consider the internal resistance of batteries, which can be simplified by treating it as a separate resistor connected in parallel with the battery. The equivalent resistance can be found by taking the reciprocal of the sum of the reciprocals of all the internal resistors.
  • #1
aznking1
16
0

Homework Statement


I have two questions. Both questions are in the picture below. Dont mind my workings lol

http://img163.imageshack.us/img163/5680/scanpic0001qe.jpg

Ans to the 1st qn: C

The potential difference across the 3ohm resistor is zero. Thus, it can be considered that the 4ohm and 2 ohm resistor is in parallel with the 8ohm and 4 ohm resistor. So the effective resistance between A and B is

(1/(4+2) +1/(8+4))^-1 = 4ohms

But my question is, why is the p.d. across 3 ohm resistor zero?

Ans to the 2nd qn: C

The effective e.m.f is 1.5v and effective internal resistance is (1/3 + 1/3+1/3)^-1 = 1ohms
E=I(R+r)
1.5=I(10 + 1)
I=0.14A

And my question is, how does the circuit work? Why do we have the consider all of the internal resistance of the batteries?
 
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  • #2


Question (1) is a typical wheatstone bridge. This bridge has potential difference in the middle resistor equal to zero if the other resistors have the relation

[tex]\frac{R_1}{R_3} = \frac{R_2}{R_4}[/tex]

Where resistors are taken R1, R3, R4, R2 clockwise from A in your diagram. You can prove this using Kirchoff's laws.

For question (2)
Every resistor is an opposition to the flow of current. Battery's internal resistance is not an exception to this. Electrons try to cross the battery and are obstructed within. So you do have to consider its resistance. To make it simpler, you can even assume it as a separate resistor just beside the battery, as it makes no difference to the problem.
 
  • #3


Question (2)
As you see all the internal resistors which normally taken as a series resistor to the emf.
All are connected at one end. The other ends all have the same potential.
So you can connect all in parallel have a single battery.
 

FAQ: Solving 2 Questions on Circuit Analysis: PD Across 3 Ohm & EMF of Batteries

1. How do I calculate the potential difference across a 3 ohm resistor in a circuit?

The potential difference (PD) across a resistor can be calculated using Ohm's Law, which states that PD = current (I) x resistance (R). In this case, the current can be found by dividing the total circuit voltage by the total resistance. Once the current is known, PD can be calculated by multiplying it by the resistance of the specific resistor (in this case, 3 ohms).

2. Can I use Kirchhoff's Voltage Law to solve for the PD across a 3 ohm resistor?

Yes, Kirchhoff's Voltage Law (KVL) can also be used to solve for the PD across a resistor. KVL states that the sum of all voltage drops in a closed loop circuit must equal the sum of all voltage sources. By setting up a loop in the circuit that includes the 3 ohm resistor, and equating the voltage drops to the voltage sources, you can solve for the PD across the resistor.

3. How do I calculate the electromotive force (EMF) of a battery?

The EMF of a battery is the maximum potential difference that it can provide to a circuit. It can be calculated by multiplying the current (I) by the internal resistance (r) of the battery and adding it to the voltage (V) across the battery terminals. Mathematically, EMF = V + Ir.

4. Can I use KVL to solve for the EMF of a battery in a circuit?

Yes, KVL can also be used to solve for the EMF of a battery. By setting up a loop in the circuit that includes the battery, and equating the voltage drops to the voltage sources, you can solve for the EMF of the battery.

5. How do I determine the polarity of the PD across a 3 ohm resistor?

The polarity of the PD across a resistor can be determined by following the direction of current flow in the circuit. The PD will be positive when the current enters the positive terminal of the resistor and negative when it exits the resistor. You can also use the passive sign convention, which states that the voltage drop across a resistor is considered positive when the current flows in the same direction as the reference direction (usually clockwise) in a circuit diagram.

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