The resistivity of manganese wire of length 1 m is 1.84 xx 10^(-6) Omega m at 20^(@) C. If the diameter of the wire is 3 xx 10^(-4) m, what will be the resistance of the wire at that temperature ? OR Observe the given circuit : Calculate the total resistance in the circuit and the total current flowing in the circuit.

The resistivity of manganese wire of length 1 m is 1.84 xx 10^(-6) Ome

1.	The resistivity of manganese wire of length 1 m is 1.84 xx 10^(-6) Omega m at 20^(@) C. If the diameter of the wire is 3 xx 10^(-4) m, what will be the resistance of the wire at that temperature ? OR Observe the given circuit : Calculate the total resistance in the circuit and the total current flowing in the circuit.
Answer» Solution :Resistivity `rho= 1.84 xx 10^(-6) Omega` m Length l = 1m DIAMETER d = `3 xx 10^(-4)` m Area of cross- section A = `(pi d^(2))/(2)` ` = (22)/(7) xx (3 xx 10^(-4) xx 3 xx 10^(-4))/(4)` = `(99)/(14) xx 10^(-8) m^(2)`. Resistance R = `(rho xx l)/(A)` = `(1.84 xx 1 xx 14 xx 10^(-6))/(99 xx 10^(-8))` ` = (22.76 xx 10^(2))/(99)` = `26.02 Omega` OR - In parallel connection, ` (1)/(R_(p)) = (1)/(R_(1)) + (1)/(R_(2)) + (1)/(R_(3)) rArr (1)/(R_(p)) = (1)/(2) + (1)/(4) + (1)/(4) ` ` rArrR_(p) = 1 Omega` . Total resistance in the CIRCUIT R = `R_(p) + R_(4)` = 1 + 5 ` = 6 Omega` `therefore" Current " I = (V)/(R) = ( 6)/(6) = 1` A .