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Twelve wires of equal length and same cross-section are connected in the form of a cube. If the resistance of each of the wires is $R$, then the effective resistance between the two diagonal ends would be
In order to measure the internal resistance $r_1$ of a cell of emf $E$, a meter bridge of wire resistance $R_0=50 \Omega$, a resistance $R_0 / 2$, another cell of emf $E / 2$ (internal resistance $r$ ) and a galvanometer $G$ are used in a circuit, as shown in the figure. If the null point is found at $l=72 cm$, then the value of $r_1=$ . . . . $\Omega$
Figure shows a simple potentiometer circuit for measuring a small $e.m.f$. produced by a thermocouple. The meter wire $PQ$ has a resistance $5 \,\Omega$ and the driver cell has an e.m.f. of $2\, V$. If a balance point is obtained $0.600\, m$ along $PQ$ when measuring an e.m.f. of $6.00\, mV$, what is the value of resistance $R$ ............... $\Omega$
A uniform heating wire of resistance $36\, \Omega$ is connected across a potential difference of $240\, {V}$ The wire is then cut into half and potential difference of $240\, {V}$ is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be $1: {x}$, where ${x}$ is........... .