356997
At what value of the resistance in the circuit shown in the figure will the total resistance between points \({A}\) and \({B}\) be independent of the number of cells? If \({R=(\sqrt{3}+1) \Omega}\), then the value of \({x}\) will be
356998
An infinite ladder network is constructed with \(1\Omega \) and \(2\Omega \) resistors as shown. Find the equivalent resistance between points \(A\) and \(B\).
1 \(1\Omega \)
2 \(2\Omega \)
3 \(3\Omega \)
4 \(0.5\Omega \)
Explanation:
Let the equivalent resistance between \(A\) & \(B\) be \(x\). The equivalent resistance across \(PQ\) is also \(x\) \({R_{AB}} = \left( {\frac{{2x}}{{2 + x}}} \right) + 1\) \(x = \frac{{2x + 2 + x}}{{2 + x}}\) \(\left( {As\;\quad {R_{AB}} = {\rm{x}}} \right)\) \(2x + {x^2} = 3x + 2\) \({x^2} - x - 2 = 0\quad \Rightarrow x = 2\Omega \)
PHXII03:CURRENT ELECTRICITY
356999
The equivalent resistance between the points \(A\) and \(B\) in the following circuit is
356997
At what value of the resistance in the circuit shown in the figure will the total resistance between points \({A}\) and \({B}\) be independent of the number of cells? If \({R=(\sqrt{3}+1) \Omega}\), then the value of \({x}\) will be
356998
An infinite ladder network is constructed with \(1\Omega \) and \(2\Omega \) resistors as shown. Find the equivalent resistance between points \(A\) and \(B\).
1 \(1\Omega \)
2 \(2\Omega \)
3 \(3\Omega \)
4 \(0.5\Omega \)
Explanation:
Let the equivalent resistance between \(A\) & \(B\) be \(x\). The equivalent resistance across \(PQ\) is also \(x\) \({R_{AB}} = \left( {\frac{{2x}}{{2 + x}}} \right) + 1\) \(x = \frac{{2x + 2 + x}}{{2 + x}}\) \(\left( {As\;\quad {R_{AB}} = {\rm{x}}} \right)\) \(2x + {x^2} = 3x + 2\) \({x^2} - x - 2 = 0\quad \Rightarrow x = 2\Omega \)
PHXII03:CURRENT ELECTRICITY
356999
The equivalent resistance between the points \(A\) and \(B\) in the following circuit is
356997
At what value of the resistance in the circuit shown in the figure will the total resistance between points \({A}\) and \({B}\) be independent of the number of cells? If \({R=(\sqrt{3}+1) \Omega}\), then the value of \({x}\) will be
356998
An infinite ladder network is constructed with \(1\Omega \) and \(2\Omega \) resistors as shown. Find the equivalent resistance between points \(A\) and \(B\).
1 \(1\Omega \)
2 \(2\Omega \)
3 \(3\Omega \)
4 \(0.5\Omega \)
Explanation:
Let the equivalent resistance between \(A\) & \(B\) be \(x\). The equivalent resistance across \(PQ\) is also \(x\) \({R_{AB}} = \left( {\frac{{2x}}{{2 + x}}} \right) + 1\) \(x = \frac{{2x + 2 + x}}{{2 + x}}\) \(\left( {As\;\quad {R_{AB}} = {\rm{x}}} \right)\) \(2x + {x^2} = 3x + 2\) \({x^2} - x - 2 = 0\quad \Rightarrow x = 2\Omega \)
PHXII03:CURRENT ELECTRICITY
356999
The equivalent resistance between the points \(A\) and \(B\) in the following circuit is
