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

In the circuit diagram given in (a), suppose the resistors R_1,R_2 and

1.	In the circuit diagram given in (a), suppose the resistors R_1,R_2 and R_3 have values 5 Omega, 10 Omega and 30 Omega respectively, which have been connected to a battery of 12 V. Calculate (a) the current through each resistor, (b) the total current in the circuit, and ( c) the total circuiot resistance.
Answer» Solution :(a) Since `R_1,R_2` and `R_3` are in parallel, the pd (V) across each ONE of them is the same, i.e., `12 V` Thus, `I_1 ("current through" R_1) = (V)/(R_1) = (12 V)/(5 Omega) = 2.4 A` `I_2 ("current through" R_2) = (V)/(R_2) = (12 V)/(10 Omega) = 1.2 A` `I_3 ("current through" R_3) = (V)/(R_3) = (12 V)/(30 Omega) = 0.4 A` (b) TOTAL current in the CIRCUIT, `I = I_1 + I_2 + I_3 = 2.4 A + 1.2 A + 0.4 A = 4 A` (c) If `R_p` is the total resistance in the circuit, then `(1)/(R_p) = (1)/(R_1) + (1)/(R_2) + (1)/(R_3) = (1)/(5) + (1)/(10) + (1)/(30) = (1)/(3)` or `R_p = 3 Omega` We can also find the total current by first calculating `R_p` and then USING, `I = (V)/(R_p)`, i.e., `I = (V)/(R_p) = (12 V)/(3 Omega) = 4 A`.