Resistances are arranged in a cyclic order to form a balanced Wheatstone bridge as shown in the figure. The ratio of power consumed in the branches $(P + Q)$ and $(R + S)$ is

  • A
    $R : Q$
  • B
    $R : P$
  • C
    $P^2 : Q^2$
  • D
    $P^2 : R^2$

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The effective resistance between points $A$ and $B$ is ............... $\Omega$.

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Two resistances $R_1 = X \Omega$ and $R_2 = 1 \Omega$ are connected to a wire $AB$ of uniform resistivity,as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 \text{ mm}$ at $A$ to $1 \text{ mm}$ at $B$. $A$ galvanometer $(G)$ connected to the center of the wire,$50 \text{ cm}$ from each end along its axis,shows zero deflection when $A$ and $B$ are connected to a battery. The value of $X$ is:

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