Question
Question: In the given circuit the internal resistance of the 18 V cell is negligible. If the\[{R_1} =400\Omeg...
In the given circuit the internal resistance of the 18 V cell is negligible. If theR1=400Ω, R3=100Ω and R4=500Ω and the reading of an ideal voltmeter across R4is 5V, then the value R2will be
A. 300Ω
B. 230Ω
C. 450Ω
D. 550Ω
Solution
In this question the value of voltage across the resistance R4is given so by using ohm's law V=IR, find the current through the resistance R4which is same as current through R3 the we will find the current through resistance R1and then find the current through the resistance R2whose resistance will be calculated.
Step by step answer: R1=400Ω
R3=100Ω
R4=500Ω
The voltage across the resistance R4 is =5V
Now we can redraw the given circuit as
Where current i is flowing through the resistance R1 which further divides into current i1 and i2, where current i1 flows through the resistances R3 and R4 whereas current i2 flows through the resistance R2,
Now consider the resistance R4 Where the voltage across through it is 5V, hence the current
i1=R4V4=5005=0.01A
We know that the current flowing through the resistances in the series is equal, hence we can say the current through the resistance R3 will be0.01A, so the voltage across the resistance R3 will be
V3=i1R3=0.01×100=1V
So the voltage across the resistances R3 and R4 will be
V=V3+V4=1+5=6V
Now we know that when resistances are connected in series then the voltage across them is equal, hence we can say voltage across the resistances R2will be same as the voltage across the resistances R3 and R4, hence we can write
V=V2=6V
From the circuit we can see the resistance R1 is in series with the parallel combination of resistances R2, R3 and R4 and the voltage across the whole circuit is 18v, hence we can write
V1+V=18V
Hence by substituting the value of voltageV=6V, we can write
So the current I through the resistanceR1=400Ω will be equal to
i=R1V1=40012=0.3A
In this circuit sincei=i1+i2, hence we can write
Therefore the Resistance of the resistor R2 will be equal to
R2=i2V=0.026=300Ω
Hence the value R2will be =300Ω Option A is correct.
Note: In these types of questions, students need to be very careful while deciding for the parallel and the series connection of the resistances. The resistances (or combination of resistances) across which the voltage is same, then the resistances are known to be parallel connected whereas the resistances through which the amount of flow of current is the same then, they are known as series connected. It is not always necessary for the resistances to be connected in series or in parallel