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In the circuit diagram given in figure s...

In the circuit diagram given in figure suppose the resistors `R_1, R_2 and R_3` have the values `5Omega, 10 Omega, 30 Omega` respectively, which have been connected to a battery of 12V. Calculate (a) the current through each resistor, (b) the total current in the circuit, and (c) the total circuit resistance.

Text Solution

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( a )`R_1 = 5Omega, R_2 = 10 Omega and R_3 = 30 Omega`.
Potential defference across the bettery, V = 12 V.
This is also the potential difference across each of the individual resistor, therefore, to calculate the current in the resistors, we use Ohm.s law.
The current `I_1`, through `R_1 = V/R_1`
`I_1 =(12 V)/(5 Omega) =2.4 A`
The current `I_2` , through `R_2 = V/R_2`
`I_2 = (12V)/(30Omega) = 0.4 A`
( b )The total current in the circuit,
`I = I_1 + I_2 +I_3`
= (2.4 + 1.2 + 0.4) A
=4 A
( c ) The total resistance `R_p`,is given by
`1/R_p = 1/5 + 1/10 + 1/30 = 1/3`
Thus, `R_P = 3 Omega`
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