The resistance of a heater coil is $110\, ohm$. A resistance $R$ is connected in parallel with it and the combination is joined in series with a resistance of $11\, ohm$ to a $220\, volt$ main line. The heater operates with a power of $110\, watt$. The value of $R$ in $ohm$ is
Diffcult
Download our app for free and get started
(a) Power consumed by heater is $110\, W$ so by using $P = \frac{{{V^2}}}{R}$
$110 = \frac{{{V^2}}}{{110}}\,\, \Rightarrow \,V = 110\,V.$ Also from figure ${i_1} = \frac{{110}}{{110}} = 1\,A$ and $i = \frac{{110}}{{11}} = 10\,A.$ So ${i_2} = 10 - 1 = 9\,A$
Applying Ohms law for resistance $R$, $V = iR$
$ \Rightarrow \,\,110 = 9 \times R$ $ \Rightarrow $ $R = 12.22\,\Omega $
$110 = \frac{{{V^2}}}{{110}}\,\, \Rightarrow \,V = 110\,V.$ Also from figure ${i_1} = \frac{{110}}{{110}} = 1\,A$ and $i = \frac{{110}}{{11}} = 10\,A.$ So ${i_2} = 10 - 1 = 9\,A$
Applying Ohms law for resistance $R$, $V = iR$
$ \Rightarrow \,\,110 = 9 \times R$ $ \Rightarrow $ $R = 12.22\,\Omega $
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance $2000 \,\Omega$ is used to measure the potential difference across $500 \,\Omega$ resister, the reading of the voltmeter will be ............... $V$View Solution
- 2Two uniform wires $A$ and $B$ are of the same metal and have equal masses. The radius of wire $A$ is twice that of wire $B$. The total resistance of A and $B$ when connected in parallel isView Solution
- 3In the circuit shown, the reading of the ammeter (ideal) is the same with both switches open as with both closed find the value of resistance $R$ in $ohm$ . ................ $\Omega$View Solution
- 4View SolutionThe internal resistance of a cell depends on
- 5The charge flowing through a resistor $R$ varies with time $t$ as $Q = 3t -6t^2.$ The heat produced in $R$ till the current in it becomes zero isView Solution
- 6Find the value of current from battery in the circuit ............... $A$View Solution
- 7An electric kettle has two heating coils. When one coil is used, water in the kettle boils in $5$ minutes, while when second coil is used, same water boils in $10\,\min$. If the two coils, connected in parallel are used simultaneously, the same water will boil in timeView Solution
- 8The terminal potential difference of a cell is greater than its $e.m.f.$ when it isView Solution
- 9The figure shows a network of resistances in which the point $A$ is earthed. The current through the $3\,\Omega$ resistor isView Solution
- 10Calculate the amount of charge flowing in $2$ minutes in a wire of resistance $10$ $\Omega$ when a potential difference of $20\,V$ is applied between its ends ............ $C$View Solution