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How would you arrange 48 cells each of e.m.f 2V and inteanal resistance $1.5 \Omega $ so as to pass maximum current through the external resistance of $2 \Omega$ ?

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Explanation

[{No of rows}/{no of cells in each row}] = (m/n) = (r/R) where r = internal resistance of each cell

R = external resistance

∴ (m/n) = {1.5/2} = (3/4)

also total number of cells = 48 m × n = 48

∴ (3/4) n × n = 48 n2 = {(48 × 4)/3} n = 8

∴ m = (48/8) = 6

∴ 6 rows with 8 cell in each of row

How many dry cells, each of emf 1.5V and internal resistance $0.5 \Omega $, much be joined in series with a resistor of $ 20 \Omega $ to give a current of 0.6A in the circuit ?

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Explanation

$ l = { n \varepsilon \over R +nr } \Leftrightarrow 0.6 = { n \times 1.5 \over 20 \times 0.5 n } \Leftrightarrow 12 + 0.3 n = 1.5 n \therefore 12 = 1.2 n $ $ \therefore n = 10 $cells to be connected in series

Two electric bulbs whose resistances are in the ratio of 1:2 are connected in parallel to a constant voltage source the power dissipated in them have the ratio.

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Explanation

$ {P_1/P_2 } = {V^2 / R_1 \over V^2 / R_2 } = {R_2 \over R_1} = 2 /1 $

An electric kettle has two coils. when onc of them is switched on, the water in the kettle boils in 6 minutes. When the other coil is switched on, the water boils in 3 minutes If the two coils are connected in series the time taken to boil water in the kettle is:

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Explanation

$H_1 = { V^2 \over R_1 } t_1$ $ R_1 = { V^2 \over H_1} t_1 and R_2 = { V^2 \over H_2 } t_2$ $ { V^2 \over H_1 } = { V^2 \over H_2 } = const \therefore R\, \alpha \,t $ $ Now R_s = R_1 + R_2 $ t = 6 + 3 = 9 Minutes

An electric kettle has two coils when one of these is switched on. the water in the kettle boils in 6 minutes. When the other coil is switched on, boils in 3 minutes If the two coils are connected in parallel, the time taken to boil water in the kettle is

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Explanation

$R_p = { R_1 R_2 \over R_1 + R_2 } $ $ t = {6 \times 3 \over 6 +3} = 2 minutes $

The potential difference between the terminals of a battery is 10V and internal resistance $1 \Omega $ drops to 8V when connected across an external resistor find the resistance of the external resistor.

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Explanation

$ V = IR \,in I = { E \over R +r } $ $ \therefore ={ ER \over R + r } $

A heater boils 1kg of water in time $t_1$ and another heater boils the same water in time $t_2$ If both are connected in series, the combination will boil the same water in time.

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At what temperature will the resistance of a copper wire be three times its value at 0°C ? (Given: temperature coefficient of resistance for copper = $4 \times 10^{-3} C^{-1}$ )

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Explanation

$R_\theta = R_\theta 0 [ 1 + \alpha ( \theta _2 - \theta _1 ) ] $ $ 3 = 1 + ( 4 \times 10 ^ {-3} ) T$ $ \therefore T = { 2 \over 4 \times 10 ^ {-3}} = 500 C $

The resistance of a copper coil is $4.64 \Omega $ at 40 °C and $5.6 \Omega$ at 100 °C Its resistcnce at 0° C will be

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Explanation

$R_{40} [1 + \alpha (\theta_2 - \theta_1)]$ $ 5.6 = 4.64[1 + a(100 -40)] =4.64+278.4 a$ $a ={5.6 -4.64 \over 278.4} = 0.0035 C^{-1}$ $ \Rightarrow _{100} = R_0(1+ \alpha T_2) = R_0 [1+(0.0035 \times 100)]$ $ 5.6 = R_0 \times 1.35$ $Ro = 4 \Omega $

There are n resistors having equal value of resistance r. First they are connected in such a way that the possible minimum value of resistance is obtained. Then they are connected in such a way that possible maximum value of resistance is obtained the ratio of minimum and maximum values of resistances obtained in these way is....

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Explanation

In parallal connection R minimum = r/n In Series connection R maximum= nr $ { R min \over R max } = { r \over n(n-1) } = {1 \over n^2}$

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