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Resistors Combination – Numerical Problem

What is the effective resistance between P and Q in the diagram?


Asked Malik Ahmed

Answer : 8 ohms

The Two arms have resistances 32 ohm and are in parallel, Their effective resistance is 1 ohms. This is in parallel with the middle arm. So the effective resistance is 8 ohms.



The three arms have resistances 32, 1 and 32 respectively and are in parallel. Therefore, taking their reciprocals and adding will give the answer.

V proportional to I or I proportional to V in Ohm’s Law?

Why we used I proportional to V?
Can we write V proportional to I also?



Both are ok. If we are changing the current and observing the voltage, then it is V∝ I

If we are changing the voltage and observing the current, then

I∝ V

In general, we write

the dependent variable proportional to the independent variable

dependent variable  = the quantity measured by us

independent variable = the quantity fixed by us

A Numerical problem from electricity

In the given diagram,the cell and the ammeter, both have negligible resistance. the resisitors are identical. With switch K open , the ammeter reads 0.6 A. What will be the ammeter reading when the switch is closed?

-Mohit asked


When the switch is open, the effective resistance is R/2, since the two resistances R each are in parallel.

Therefore, the pd, V = I x R/2 = 0.6 x R/2 = 0.3 R

When the key is closed, the effective resistance becomes R/3

Now the reading of the ammeter, I’ = V/(R/3) = 0.3R/(R/3)=0.9A

Conversion of Galvanometer to Ammeter problem

Diagram of D'Arsonval/Weston type galvanometer.
Diagram of D'Arsonval/Weston type galvanometer. (Photo credit: Wikipedia)

A galvanometer can be converted to ammeter by connecting a low resistance, called shunt in parallel with it. If a galvanometer of resistance 45 Ω is shunted by a resistance of 5 Ω what fraction of main current passes through the  Galvanometer? What is the current which flows through the shunt?


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