In the figure shown below, if the maximum possible unknown resistance X (in Ω ), that can be measured by the post office box is given by a×10bΩ in scientific notation, then find the value of a−b. (In this experiment, we take out only one plug in arm AB and only one plug in arm BC, but in arm AD we can take out many plugs).

By Wheastone bridge principle, we have PQ=RX or X=RQPNow, Xmax=RmaxQmaxPmin Xmax=9000×100010=9×105

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In the figure shown below, if the maximum possible unknown resistance X (in $Ω$ ), that can be measured by the post office box is given by $a \times 10^{b} Ω$ in scientific notation, then find the value of $a - b .$ (In this experiment, we take out only one plug in arm AB and only one plug in arm BC, but in arm AD we can take out many plugs).

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Detailed Solution

By Wheastone bridge principle, we have $\frac{P}{Q} = \frac{R}{X} o r X = \frac{R Q}{P}$
Now, $X_{\max} = \frac{R_{\max} Q_{\max}}{P_{\min}}$
$X_{\max} = \frac{9000 \times 1000}{10} = 9 \times 10^{5}$

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