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The charge flowing through a resistance $R$ varies with time as $Q = 2t - 8t^2$. The total heat produced in the resistance is (for $0 \leq t \leq \frac{1}{8}$)
In an experiment to measure the internal resistance of a cell by potentiometer, it is found that the balance point is at a length of $2\,m$ when the cell is shunted by a $5\,\Omega $ resistance; and is at a length of $3\,m$ when the cell is shunted by a $10\,\Omega $ resistance. The internal resistance of the cell is, then ................ $\Omega $
A battery of internal resistance $4\,\Omega $ is connected to the network of the resistance as shown in Fig. If the maximum power can be delivered to the network, the magnitude of $R$ in $\Omega $ should be
In the given circuit, the current flowing through the resistance $20\ \Omega$ is $0.3 \mathrm{~A}$, while the ammeter reads $0.9 \mathrm{~A}$. The value of $\mathrm{R}_1$ is_____________ $\Omega$.
In the circuit shown the variable resistance is so adjusted that the ammeter reading is same in both the position $1$ and $2$ of the key. The reading of ammeter is $2A$. If $E = 20V$, then $x$ is :- ................... $\Omega$
A circuit containing five resistors is connected to a battery with a $12 \,V$ emf as shown in figure. The potential difference across $4 \,\Omega$ resistor is ........... $V$
In an aluminium $(A1)$ bar of square cross section, a square hole is drilled and is filled with iron ( $Fe$ ) as shown in the figure. The electrical resistivities of $A 1$ and $Fe$ are $2.7 \times 10^{-8} \ \Omega m$ and $1.0 \times 10^{-7} \ \Omega m$, respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is