Using Kirchoff's rule, determine the value of the unknown resistance $R$ in the circuit Figure so that no current flows through a $4\Omega$ resistance. Also find the potential difference between $A$ and $D$.

 

In the circuit shown in Fig.$5.159,$ Assuming point $A$ To be at zero potential, use Kirchhoff's rules to determine the potential at $B.$

Use Kirchhoff's rules to write the expressions for the currents $I_{1,}{I}_2$ and $I_3$ In the circuit diagram shown in Fig.$5.160.$

Use Kirchoff's rules to loops $ACBPA$ and $ACBQA$ to write the expressions for the currents, $I_1,I_2$ and $I_3$ in the network shown in Figure

Use Kirchhoff's laws, calculate the potential difference across the $8\Omega$ Resistor in the circuit of Fig.$5.161.$

A battery $E_1$ of $4V$ And a variable resistance $Rh$ Are connected in series with the wire $AB$ Of the potentiometer Fig.$5.162.$ The length of the wire of the potentiometer is $1$ Metre. When a cell $E_2$ Of emf $1.5V$ Is connected between $A$ and $C,$ No current flows through $E_2$, Length of $AC=60 cm,$

(i) Find the potential difference between the ends $A$ and $B$ Of the potentiometer,

A battery $E_1$ of $4V$ And a variable resistance $Rh$ Are connected in series with the wire $AB$ Of the potentiometer Fig.5.162.5.162. The length of the wire of the potentiometer is 11 metre. When a cell $E_2$ Of emf $1.5V$ Is connected between $A$ and $C,$ No current flows through $E_2$, Length of $AC=60 cm,$

(ii) would the method work if the battery $E_1$ Is replaced by a cell of emf $1V$ ?

The figure, Fig. $5.163$ Shows a potentiometer with a cell of $2.0 \mathrm{V}$ And internal resistance $0.40\Omega$ Maintaining a potential.

Drop across a resistor wire $\mathrm{AB}$ A standard cell which maintains a constant emf of $1.02 \mathrm{V}$ (for very moderate current currents up to a few $\mu \mathrm{A}$ ) gives a balance point at $67.3 \mathrm{cm}$ Length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of $600\mathrm{k}\Omega$ Is put in series with it, which is shorted close to balance point. The standard cell is then replaced by a cell of unknown emf $\in$ And the balance point found similarly turns out to be at $82.3 \mathrm{cm}$ Length of the wire.

(a) What is the value of $\in$?