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Draw a schematic diagram of a circuit consisting of a battery of 3 cells of 2 V each, a combination of three resistors of 10 W, 20 W, and 30 W connected in parallel, a plug key, and an ammeter, all connected in series. Use this circuit to find the value of the following :(a) Current through each resistor.(b) Total current in the circuit.(c) Total effective resistance of the circuit.
Given:
Resistance, $R_1=10\Omega$
Resistance, $R_2=20\Omega$
Resistance, $R_3=30\Omega$
Number of cells $=3$
Voltage of each cell =2 V
Total volatgeof the battery, $V=2\times {3}=6V$
To find: (a) Current through each resistor.
(b) Total current in the circuit.
(c) Total effective resistance of the circuit.
Solution: (c) Total effective resistance of the circuit.
Here, all the resistance is given in parallel.
So, the total resistance is given by-
$\frac {1}{R_E}=\frac {1}{R_1}+\frac {1}{R_2}+\frac {1}{R_3}$
$\frac {1}{R_E}=\frac {1}{10}+\frac {1}{20}+\frac {1}{30}$
$\frac {1}{R_E}=\frac {6+3+2}{60}$
$\frac {1}{R_E}=\frac {11}{60}$
$\frac {1}{R_E}=\frac {11}{60}$
$R_E=\frac {60}{11}$
$R_E=5.45\Omega$
Thus, the total effective resistance, $R_E$ is 5.45 Ohm
Solution: (b) Total current in the circuit.
Now, we know that the total current in the circuit is given as-
$I=\frac {V}{R}$
Substituting the value of $V$ and $R$ we get-
$I=\frac {6}{5.45}$
$I=\frac {6\times {100}}{545}$
$I=\frac {600}{545}$
$I=1.1A$
Thus, the total current, $I$ in the circuit is 1.1 Ampere.
Solution: (a) Current through each resistor.
Let the current is $I_1$, $I_2$ and $I_3$ in the resistance $R_1$, $R_2$ and $R_3$.
We know that, in parallel combination, the voltage remains the same across each resistor.
Current $I$, in the circuit is given by the formula-
$I=\frac {V}{R}$
Substituting the given values we get-
$I_1=\frac {V}{R_1}\Rightarrow\frac {6}{10}\Rightarrow0.6A$
$I_1=\frac {V}{R_2}\Rightarrow\frac {6}{20}\Rightarrow0.3A$
$I_1=\frac {V}{R_3}\Rightarrow\frac {6}{30}\Rightarrow0.2A$
Thus,
(a) Current through each resistor - 0.6A, 0.3A, 0.2A.
(b) Total current in the circuit - 1.1 Ampere.
(c) Total effective resistance of the circuit - 5.45 Ohm.
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