Sheet 06 Temp. Co-efficient of Resistance and Colour Coding.
A carbon resistor has coloured strips \(1^{st}\), \(2^{nd}\), \(3^{rd}\) and \(4^{th}\) as follows Yellow, Violet, Brown and Gold respectively. What is its resistance?
Ans: \(\left(470\Omega\pm 5\%\right)\).
How will you represent a resistance of \(3700\Omega\pm10\%\) by colour code?
Ans:orange, violet, red and silver.
A voltage of \(6V\) is applied across a colour coded carbon resistor with first, second and third bands are brown, black and red colours. What is the current flowing through the given resistor?
Ans: \(0.6mA\).
The sequence of band marked on a carbon resistor are yellow, red, orange and silver. What is (i) its resistance. (ii) tolerance. and (iii) Range of resistance.
Ans:(i) \(R=\left(42\times 10^{3}\right)\Omega\). (ii) \(\pm 10\%\) (iii) \(\left(46200\Omega – 37800\Omega\right)\).
A tungsten coil has a resistance of \(12\Omega\) at \(15^{o}C\). If, the temperature co-efficient of resistance of tungsten is \(0.004^{o}C^{-1}\), Calculate: the resistance of the coil at \(80^{o}\).
Ans: \(R_{80}=15\Omega\).
A nichrome heating element connected to a \(220V\) supply draws an initial current of \(2.2A\) which settles down after a few seconds to a steady value of \(2.0A\). Find: the steady temperature of the heating element. The room temperature is \(30^{o}C\) and the average temperature coefficient of resistance of nichrome is \(\left(1.7\times10^{-4}\right)^{o} C^{-1}\).
Ans: \(T_{steady}=618^{o}C\).
The resistance of a platinum wire of platinum resistance thermometer at the ice point is \(5\Omega\) and at steam point is \(5.23\Omega\). When the thermometer is inserted in a hot bath, the resistance of the platinum wire is \(5.795\Omega\). Calculate: temperature of the hot bath.
Ans: \(T=345.65^{o}C\).
The resistance of a conductor at \(20^{o}C\) is \(3.15\Omega\) and at \(100^{o}C\) is \(3.75\Omega\). Determine the temperature co-efficient of resistance of the conductor. What will be the resistance of the conductor at \(0^{o}C\).
Ans: \(R_{0^{o}C}=3.0\Omega\).
A potential difference of \(120V\) is applied to a coil at the temperature of \(12^{o}C\) and the current is \(6A\). What will be the mean temperature of the coil when the current has fallen to a value \(3A\), the applied voltage being the same as before? Given: Temperature Co-efficient of resistance of coil is \(0.00427^{o}C^{-1}\) at \(0^{o}C\).
Ans: \(T_{mean}=258^{o}C\).
Resistivity of the material of a conductor of uniform cross-section varies along its length as \(\rho=\rho_{o}\left(1+\alpha x\right)\). Find: the resistance if its length is L and area of cross-section is A.
The temperature coefficient of resistivity for two materials A and B are \(0.0031^{o}C^{-1}\) and \(0.0068^{o}C^{-1}\) respectively. Two resistors \(R_{1}\) and \(R_{2}\) made from material A and B respectively, have resistance \(200\Omega\) and \(100\Omega\) at \(0^{o}C\). Show on a diagram, the colour code of a carbon resistor, that would have a resistance equal to the series combination of \(R_{1}\) and \(R_{2}\), at temperature \(100^{o}C\). (Neglect: the ring corresponding to the tolerance of carbon resistor).
A heating element using nichrome connected to \(230V\) supply draws a current of \(3.2A\) which settles after few seconds to a steady value of \(2.8A\). What is the steady temperature of heating element if the room temperature is \(27^{o}C\)? Temperature co-efficient of resistivity of nichrome averaged over the temperature range involved is \(\left(1.70\times10^{-4}\right)^{o}C^{-1}\).
Ans: \(T_{steady}=867^{o}C\).
The resistance of iron and copper wires at \(20^{o}C\) are \(4.1\Omega\) and \(4.3\Omega\) respectively. At what temperature will the resistance be equal? Temperature coefficient of resistance foe iron is \(5.0\times10^{-3}K^{-1}\) and for copper is \(4.0\times10^{-3}K^{-1}\). Neglect any thermal expansion.
