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Electricity Test - 31

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Electricity Test - 31
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  • Question 1
    1 / -0
    If the equivalent resistance is to be increased, then the number of resistances should be connected in:
    Solution
    Equivalent resistance is maximum and current flow is minimum when number of resistances are connected in series.$$R_{eq}= R_1 + R_2 + R_3$$   ; where $$R_1,R_2,R_3$$ are resistances.
  • Question 2
    1 / -0
    Why is electrical wiring usually made from copper?
    Solution
    Materials that allow an electric current to pass through them are called
    conductors. Copper is a good conductor of electricity. The electrical wiring usually made from copper because copper conducts electricity.
  • Question 3
    1 / -0
    The equivalent resistance due to series connection of $$10\ \Omega$$ and $$10\ \Omega$$ resistors is 
    Solution
    For series connection(Current remains same): 
    $$R_{ (total)} = R_1 + R_2$$
    In series combination equivalent resistance is total sum of the resistances.
    $$\Rightarrow R_{total}=10+10$$
    $$\Rightarrow R_{total}=20\Omega $$
  • Question 4
    1 / -0
    In any electric circuit, when the switch is on and the current is flowing through it why do the wire, switches, bulb or devices in the circuit become hot?
    Solution
    This is because some of the electric energy is converted into heat energy, i.e., heating effect of electric current.
  • Question 5
    1 / -0
    In the series combination of two or more than two resistances.
    Solution
    For resistances in series, the current through each resistors remains the same.
  • Question 6
    1 / -0
    A light bulb is rated at 100 W for a 220 V ac supply. The resistance of the bulb is then
    Solution
    Here, P =  100 W , $$V \, = \, 220 \, V $$
    Resistance of the bulb is 
    $$R \, = \, \dfrac{V^{2}}{P} \, = \, \dfrac{(220)^2}{100} \, = \, 484 \, \Omega$$
  • Question 7
    1 / -0
    If five equal pieces of $$25\Omega$$ are connected in parallel, then their equivalent resistance will be............
    Solution
    Resistance of each piece :
    $$R_1 = R_2=R_3=R_4 = R_5 = 25 \ \Omega$$
    Equivalent resistance in parallel  
    $$\dfrac{1}{R_p} = \dfrac{1}{R_1}+\dfrac{1}{R_2} +\dfrac{1}{R_3}+\dfrac{1}{R_4}+\dfrac{1}{R_5}$$
    $$\therefore$$    $$\dfrac{1}{R_p} = \dfrac{1}{25}+\dfrac{1}{25} +\dfrac{1}{25}+\dfrac{1}{25}+\dfrac{1}{25}$$
    $$\implies \ \dfrac{1}{R_p} = \dfrac{5}{25}$$
    We get,
    $$R_p = 5\Omega$$
  • Question 8
    1 / -0
    In a house, individual powers of two elements are $$100\ W\ 100\ W$$. The effective power of their series combination will be :
    Solution
    $$\begin{array}{l}I = \dfrac{V}{{{R_1}}}\\{I^2}R = 100\\I' = \dfrac{V}{{{R_2}}}\\I{'^2}{R_2} = 150\\{R_1} = \dfrac{{100}}{{{I^2}}}\\{R_1} = \dfrac{{100}}{{{{\left( {V/{R_1}} \right)}^2}}}\\{R_1} = \dfrac{{{V^2}}}{{100}}\\{R_2} = \dfrac{{{V^2}}}{{150}}\\{R_1} + {R_2} = {V^2}\left( {\dfrac{1}{{100}} + \dfrac{1}{{150}}} \right)\\{R_3} = {V^2}\dfrac{5}{{100}} = \dfrac{{{V^2}}}{{60}}\\effective\,power = \dfrac{{{V^2}}}{{{R_3}}} = \dfrac{{{V^2}}}{{\left( {{V^2}/60} \right)}} = 60W\end{array}$$
  • Question 9
    1 / -0
    Combine three resistors $$5\Omega, 4.5\Omega$$ and $$3\Omega$$ in such a way that the total resistance of this combination is maximum:
    Solution
    Given resistance,
    $$R_1=5\Omega\\R_2=4.5\Omega\\R_1=3\Omega$$

    In series combination effective resistance will be maximum.
    ie, $$R_{eq}=R_1+R_2+R_3$$
         $$R_{eq}=5 \Omega + 4.5 \Omega + 3 \Omega = 12.5 \Omega$$

    Option A
  • Question 10
    1 / -0
    The smallest resistance that can be obtained by combining 10 resistors each of resistance $$10 \Omega$$ is
    Solution
    When the resistors are connected in parallel combination, the equivalent resistance will decrease. Thus, if the 10 resistors are connected in parallel, we will get minimum resistance.
    Thus, $$\dfrac{1}{R_{eq}}=\dfrac{n}{R}$$  where $$n=10$$ number of resistors which have same resistance and $$R=10 \Omega$$ resistance of each resistor.
    So, $$\dfrac{1}{R_{eq}}=\dfrac{10}{10}$$
    or $$R_{eq}=1$$
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