If in figure, R_1 = 10 Omega,R_2=40 Omega, R_3 = 30 Omega, R_4 = 20 Omega, R_5 = 60 Omega a 12 V battery is connected to the arrangement. Calculate ( a ) the total resistance in the circuit and ( b ) the total current flowing in the circuit.

If in figure, R_1 = 10 Omega,R_2=40 Omega, R_3 = 30 Omega, R_4 = 20 Om

1.	If in figure, R_1 = 10 Omega,R_2=40 Omega, R_3 = 30 Omega, R_4 = 20 Omega, R_5 = 60 Omega a 12 V battery is connected to the arrangement. Calculate ( a ) the total resistance in the circuit and ( b ) the total current flowing in the circuit.
Answer» SOLUTION :( a ) Suppose, we replace the parallel resistors `R_1 and R_2` by an eqUivalent resistor of resistance, R.. Similarly we replace the parallel resistors `R_3,R_4 and R_5`by an eqUivalent single resistor of resistance R". Then using equation of equivalent resistance of parallel combination of resistances, we have `1/(R.) = 1/10 +1/40 =5/40 , " that is " R. = 8 OMEGA` Similarly, `1/(R.) = 1/30 + 1/20 + 1/60 + 6/60` , that is,`R.. =1 0Omega` Thus, the total resistance,R = R. + R.. = `18 Omega` ( b ) To CALCULATE teh current, we use the Ohm.s law, and get `I = V/R =(12V)/(18Omega) = 0.67 A`.