A student has three \(6.0~\Omega\) resistors that can be connected together in any configuration. What are the maximum and minimum resistance that can be obtained by using one or more of these three resistors?
(Assume the connections between the resistors have negligible resistance, the temperature of the resistors is constant, and the resistors are used in a d.c. circuit and none of the resistors are short­circuited.)

1. maximum resistance: \(12~\Omega\); minimum resistance: \(0.50~\Omega\)
2. maximum resistance: \(6.0~\Omega\); minimum resistance: \(0.50~\Omega\)
3. maximum resistance: \(18~\Omega\); minimum resistance: \(6.0~\Omega\)
4. maximum resistance: \(18~\Omega\); minimum resistance: \(2.0~\Omega\)

Subtopic:  Combination of Resistors |
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A circuit consists of five identical conductors as shown in the figure. The two similar conductors are added as indicated by the dotted lines. The ratio of resistances before and after addition will be:
     
1. \(7/5\)
2. \(3/5\)
3. \(5/3\)
4. \(6/5\)
Subtopic:  Combination of Resistors |
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The equivalent resistance between \(A\) and \(B\) for the mesh shown in the figure is:

      

1. \(7.2\) \(\Omega\) 2. \(16\) \(\Omega\)
3. \(30\) \(\Omega\) 4. \(4.8\) \(\Omega\)
Subtopic:  Combination of Resistors |
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The circuit shown contains three identical resistors, two ammeters \(X\) and \(Y\), and a voltmeter \(Z\). The internal resistance of the battery is negligible.
         
Which option shows the readings on the three meters?
(Assume the ammeters have negligible resistance, and negligible current flows through the voltmeter.)

1. \(X= 1.0~\text{A}; Y = 0.0~\text{A}; Z= 12~\text{V}\)
2. \(X= 2.0~\text{A}; Y = 0.0~\text{A}; Z= 4.0~\text{V}\)
3. \(X= 1.0~\text{A}; Y = 2.0~\text{A}; Z= 8.0~\text{V}\)
4. \(X= 3.0~\text{A}; Y =6.0~\text{A}; Z= 12~\text{V}\)
Subtopic:  Combination of Resistors |
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The equivalent resistance between points \(A\) and \(B\) in the circuit shown in the figure is:

                            

1. \(6R\)

2. \(4R\)

3. \(2R\)

4. \(R\)

Subtopic:  Combination of Resistors |
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What is the equivalent resistance between \(A\) and \(B\) in the figure below if \(R= 3~\Omega?\)
                    
1. \(9~\Omega\)
2. \(12~\Omega\)
3. \(15~\Omega\)
4. None of these

Subtopic:  Combination of Resistors |
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A potential divider is used to give outputs of \(2~\text{V}\) and \(3~\text{V}\) from a \(5~\text{V}\) source, as shown in the figure.

        

Which combination of resistances, from the ones given below, \(R_1, R_2, ~\text{and}~R_3\) give the correct voltages?
1. \({R}_1=1~\text{k} \Omega, {R}_2=1 ~\text{k} \Omega, {R}_3=2 ~\text{k} \Omega\)
2. \({R}_1=2 ~\text{k} \Omega, {R}_2=1~\text{k} \Omega, {R}_3=2~\text{k} \Omega\)
3. \({R}_1=1 ~\text{k} \Omega, {R}_2=2~ \text{k} \Omega, {R}_3=2~ \text{k} \Omega\)
4. \({R}_1=3~\text{k} \Omega, {R}_2=2~\text{k} \Omega, {R}_3=2~ \text{k} \Omega\)
Subtopic:  Combination of Resistors |
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In the circuit shown in the figure, the effective resistance between \(A\) and \(B\) is:

                             

1. \(2~\Omega\)
2. \(4~\Omega\)
3. \(6~\Omega\)
4. \(8~\Omega\)

Subtopic:  Combination of Resistors |
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The effective resistance between points \(P\) and \(Q\) of the electrical circuit shown in the figure is:
              
1. \(\frac{2 R r}{\left(R + r \right)}\)
2. \(\frac{8R\left(R + r\right)}{\left( 3 R + r\right)}\)
3. \(2r+4R\)
4. \(\frac{5R}{2}+2r\)

Subtopic:  Combination of Resistors |
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The resistance between points \(A\) and \(B\) in the circuit shown in the following figure is:
           
1. \(10~\Omega\)
2. \(20~\Omega\)
3. \(30~\Omega\)
4. \(40~\Omega\)
Subtopic:  Combination of Resistors |
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