Question

câu 1 : cho hai điện trở R1 và R2 CMR:

a, khi R1 nối tiếp R2 thì\(\dfrac{U1}{U2}=\dfrac{R1}{R2}\)VÀ\(\dfrac{Q1}{Q2}=\dfrac{R1}{R2}\)

b, khi R1//R2 thì\(\dfrac{I1}{I2}=\dfrac{R2}{R1}\)VÀ\(\dfrac{Q1}{Q2}=\dfrac{R1}{R2}\)

HELP ME

Answer 1

a, Taco: R1= U1/I1 ; R2= U2/I2

=> I1 = U1/R1 ; I2 = U2/R2

mà I1=I2 => U1/R1 = U2/R2

=> U1/U2 = R1/R2 (1)

Ta co: Q1= U1.I1.t ; Q2 = U2.I2.t

=> \(I1=\dfrac{Q1}{U1.t};I2=\dfrac{Q2}{U2.t}\)

=> \(\dfrac{Q1}{U1.t}=\dfrac{Q2}{U2.t}\Rightarrow\dfrac{Q1}{Q2}=\dfrac{U1.t}{U2.t}\)(2)

(1) (2) => Q1/Q2 = R1/R2

b, Ta co: I1 = U1/R1 ; I2 = U2/R2

=> \(\dfrac{I1}{I2}=\dfrac{U1}{R1}:\dfrac{U2}{R2}=\dfrac{U1.R1}{U2.R2}\)

mà U1 = U2 => I1/I2 = R1/R2

\(I1=\dfrac{Q1}{U1.t};I2=\dfrac{Q2}{U2.t}\)

=> \(\dfrac{I1}{I2}=\dfrac{Q1}{U1.t}:\dfrac{Q2}{U2.t}=\dfrac{Q1}{Q2}\)

=> Q1/Q2 = R1/R2