Current Electricity (12Acd04)

Sheet 04 Combination of Resistances.

1. A circular ring of having negligible resistance is used to connect four resistances \(6R\), \(6R\), \(6R\) and \(R\) as shown in figure. Find: the equivalent resistance between point A and B?
   
   
   Ans: \(R_{AB}=3\times R\).
   
   
2. Find: the effective resistance of the network between points X and Y when (i) the switch is open. (ii) when switched is closed.
   
   
   Ans: (i) \(R_{eff}=9\Omega\) and (ii) \(R_{eff}=8\Omega\).
   
   
3. In the given circuit; with steady current, calculate the potential difference across the capacitor and the charge stored in it.
   
   
   Ans: \(V_{c}=2V\) and \(Q=2\mu C\).
   
   
4. In the given circuit shown below. \(R_{1}=4\Omega\), \(R_{1}=R_{3}=15\Omega\), \(R_{4}=30\Omega\) and \(E=10V\). Work out the equivalent resistance of the circuit and the current in each resistor.
   
   
   Ans: \(R_{eff}=10\Omega\) and \(I_{1}=1A\), \(I_{2}=0.4A\), \(I_{3}=0.4A\) & \(I_{4}=0.2A\).
   
   
5. In the given circuit shown, find the current through each resistor.
   
   
   Ans: \(I_{4.5\Omega}=I_{0.5\Omega}=I_{1.0\Omega}=0.5A\) and \(I_{3.0\Omega}=0.33A\) & \(I_{6.0\Omega}=0.17A\).
   
   
6. The reading of the (Ideal) ammeter in the circuit shown here, equals.
   (i) I when key \(K_{1}\) is closed and key \(K_{2}\) is open.
   (ii) \(\frac{I}{2}\) when both \(K_{1}\) and \(K_{2}\) are closed.
   Find: the expression for the resistance of X in terms of resistance of R and S.
   
   
   Ans: \(X=\frac{RS}{R-S}\).
   
   
7. In the circuit given below, find the volt-meter reading across \(4\Omega\) resistor.
   
   
   Ans:\(V_{4\Omega}=4V\).
   
   
8. In the circuit given below. Find the value of current through the ammeter A.
   
   
   Ans: \(I_{ammeter}=0.25A\).
   
   
9. Find: the value of the current in the circuit shown in below figure.
   \(\)Find: the value of the current in the circuit shown in below figure.
   Ans: \(0.1A\).
   
   
10. A wire of resistance \(8R\) is bent into a form of circle. What is the effective resistance between the ends of diameter AB?
    
    
    Ans: \(2R\).
    
    
11. Two identical slabs, of a given metal, are joined together in two different ways, as shown in figures. What is the ratio of the resistances of two combination?
    
    
    Ans: \(\frac{4}{3}\).
    
    
12. If the reading of ammeter \(A_{1}\) in below figure is \(24A\) what will be the ammeters \(A_{2}\) and \(A_{3}\) read? Neglect resistance of Ammeter.
    
    
    Ans: \(1.6A, 4.0A\).