In the meter bridge experimental set up is shown below , the null point D is obtained at a distance of \(40cm\) from end A of the meter bridge wire when a resistor of \(10\Omega\) is connected is series with \(R_{1}\).And if, a resistor of \(10\Omega\) is connected in series with \(R_{2}\), null point is obtained at \(AD=60cm\). Calculate: Value of \(R_{1}\) and \(R_{2}\)?
Ans:\(R_{1}=8\Omega\) and \(R_{2}=12\Omega\).
In a meter bridge, the null point is found at a distance of \(40cm\) from end A. If, a resistor of \(12\Omega\) is connected parallel to S, the null point occurs at \(50cm\) from end A. Determine: the value of \(R\) and \(S\)?
Ans: \(R=4\Omega\) and \(S=6\Omega\).
When two unknown resistances R and S are connected in left and right gap of the metre bridge, the balance point is found to be at a distance \(l_{1}\) from the zero mark of the metre bridge wire. An unknown resistance X is now connected in parallel to the resistance S and the balance point is found at a distance \(l_{2}\) from the zero end of the metre bridge wire. Obtain: a formula for X in terms of \(l_{1}\), \(l_{2}\) and \(S\).
Below figure shows an experimental setup of a metre bridge. The null point is to be \(60cm\) away from end A with \(X\) and \(Y\) in position as shown. When a resistance of \(15\Omega\) is connected in series with Y, the null point shifts by \(10cm\) towards the end A of the wire. Find: the position of null point if a resistance of \(30\Omega\) were connected in parallel with Y?
Ans:\(l=75cm\).
In given diagram, the experimental setup of a metre bridge is shown, When the two unknown resistances X and Y are inserted, the null point Dis obtained \(40cm\) from end A. When resistance of \(10\Omega\) is connected in series with X, the null point shifts by \(10cm\). Find: the position of the null point when the \(10\Omega\) resistance is connected in series with resistance Y. Determine: the value of \(X\) and \(Y\).
Ans: \(l^{‘}=\frac{2}{3}m\) and \(R_{2}=4\Omega\).
Two cells of e.m.f \(E_{1}\) and \(E_{2}\) \(\left(E_{1}>E_{2}\right)\) are connected between A and B the balancing length of the potentiometer wire is \(300cm\). On connecting the same potentiometer between A and C, the balancing length is \(100cm\). Calculate: the ratio of \(E_{1}\) and \(E_{2}\).
Ans: \(\frac{E_{1}}{E_{2}}=\frac{3}{2}\).
The length of the potentiometer wire is \(5m\). It is connected to a battery of constant e.m.f. For a given Laclanche Cell, the position of the zero galvanometer deflection is obtained at \(100cm\). If, the length of the potentiometer wire be made \(8m\) instead of \(5m\). Calculate: the length of the wire for zero deflection in the galvanometer for the same cell.
Ans: \(l_{1}^{‘}=1.6m\).
In a potentiometer, a standard cell of e.m.f \(5V\) and of negligible internal resistance maintains a steady current through the potentiometer wire of length \(5m\). Two primary cells of e.m.f \(E_{1}\) and \(E_{2}\) are joined in series with (i) same polarity, and (ii) opposite polarity. The combination is now connected trough a galvanometer and jockey to the potentiometer. The balancing lengths in two cases are found to be \(350cm\) and \(50cm\) respectively. (i) Draw the necessary circuit diagram. (ii) Find, the value of e.m.f of two cells.
Ans: \(E_{1}=2.0V\) and \(E_{2}=1.5V\).
A \(10m\) long wire of uniform cross-section of \(20\Omega\) is used as a potentiometer wire. This wire is connected in series with a battery of \(5V\) along with the an external resistance of \(480\Omega\). If the unknown e.m.f \(E\) is balanced at \(600cm\) of the wire. Calculate: (i) The value of the potentiometer gradient of the potentiometer. (ii) The value of unknown e.m.f?
Ans: \(K=0.00002V.cm^{-1}\) and \(e.m.f=0.12V\).
A long potentiometer wire AB is having a constant potential gradient along its length. The null points for two primary cells \(E_{1}\) and \(E_{2}\) connected in a manner shown in below figure are obtained at a distance of \(120cm\) and \(300cm\) from the point A. Find: (i) \(\frac{E_{1}}{E_{2}}\) and (ii) Position of the null point for the cell \(E_{1}\). Ans: \(\frac{E_{1}}{E_{2}}=\frac{7}{3}\). and Null point for cell \(E_{1}\) \(210cm\).
In the circuit diagram shown below, AB is uniform wire of resistance \(15\Omega\) and length \(1m\). It is connected to a cell \(E_{1}\) of e.m.f of \(2V\) and negligible internal resistance \(R\). The balance point with another cell of e.m.f \(E_{2}\) of e.m.f \(75mV\) is found at \(30cm\) from end A. Calculate: value of R.
Ans: \(R=105\Omega\).
In the following potentiometer circuit AB is a uniform wire of length \(1m\) and resistance \(10\Omega\). Calculate: the potential gradient along the wire and balanced length \(AO\left(l\right)\) when galvanometer shows no deflection.
Ans: \(K=\left(\frac{dv}{dl}\right)=\frac{4}{5}V.m^{-1}\) and \(L_{balanced}=0.375m\).
A resistance of \(R\Omega\) draws a current from potentiometer. The potentiometer has a total resistance of \(R_{o}\Omega\). A voltage of \(V\) is supplied to the potentiometer. Derive an equation for the voltage fed into the circuit when the slide is in the middle of the potentiometer.
Ans: \(R=105\Omega\).
A potentiometer wire of length \(1.0m\) has a resistance of \(15\Omega\) It is connected in series with a resistance of \(5\Omega\). Determine: the e.m.f of the primary cell which gives the balance point of \(60cm\).
Ans: \(E=1.35V\)
What is end error in a meter bridge ? How is it overcome? The resistances in the two arms of the meter bridge are \(R=5\Omega\) and \(S\) respectively. When the resistance S is shunted with an equal resistance, the new balance length found to be \(1.5l_{1}\), where \(l_{1}\) is the initil balancing length. Calculate: the value of S.
