Question
Find the value of a+b in the given figure
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/478061/1/951206/Picture57.png)
The correct answer is: ![180 to the power of ring operator end exponent](data:image/png;base64,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)
Related Questions to study
In the figure, the potentiometer wire AB of length L and resistance 9r is joined to the cell D of emf e and internal resistance r. The cell C's emf is
and is internal resistance is 2r. The galvanometer G will show no deflection when the length AJ is
![](data:image/png;base64,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)
In the figure, the potentiometer wire AB of length L and resistance 9r is joined to the cell D of emf e and internal resistance r. The cell C's emf is
and is internal resistance is 2r. The galvanometer G will show no deflection when the length AJ is
![](data:image/png;base64,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)
By error, a student places moving–coil voltmeter V (nearly ideal) in series with the resistance in a circuit in order to read the current, as shown. The voltmeter reading will be
![](data:image/png;base64,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)
By error, a student places moving–coil voltmeter V (nearly ideal) in series with the resistance in a circuit in order to read the current, as shown. The voltmeter reading will be
![](data:image/png;base64,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)
In the figure shown the power generated in y is maximum when
then R is
![](data:image/png;base64,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)
In the figure shown the power generated in y is maximum when
then R is
![](data:image/png;base64,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)
A battery of internal resistance 4W is connected to the network of resistance as shown. In order that the maximum power can be delivered to the network, the value of R in W should be :–
![](data:image/png;base64,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)
A battery of internal resistance 4W is connected to the network of resistance as shown. In order that the maximum power can be delivered to the network, the value of R in W should be :–
![](data:image/png;base64,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)
Identify the functional groups in the following compound.
![](data:image/png;base64,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)
Identify the functional groups in the following compound.
![](data:image/png;base64,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)
Three 60W, 120V light bulbs are connected across a 120 V power source. If resistance of each bulb does not change with current then find out total power delivered to the three bulbs.
![](data:image/png;base64,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)
Three 60W, 120V light bulbs are connected across a 120 V power source. If resistance of each bulb does not change with current then find out total power delivered to the three bulbs.
![](data:image/png;base64,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)
For natural numbers m,n if
and
then (m,n) is
For natural numbers m,n if
and
then (m,n) is
In the circuit shown the capacitor of capacitance C is initially uncharged. Now the capacitor is connected in the circuit as shown. The charge passed through an imaginary circular loop parallel to the plates (also circular) and having the area equal to half of the area of the plates, in one time constant is:
![](data:image/png;base64,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)
In the circuit shown the capacitor of capacitance C is initially uncharged. Now the capacitor is connected in the circuit as shown. The charge passed through an imaginary circular loop parallel to the plates (also circular) and having the area equal to half of the area of the plates, in one time constant is:
![](data:image/png;base64,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)
is divisible by_____ in N
is divisible by_____ in N
A potential divider is used to give outputs of 2V and 3V from a 5V source, as shown in figure. Which combination of resistances, R1 , R2 and R3 gives the correct voltages?
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/477834/1/950928/Picture10.png)
A potential divider is used to give outputs of 2V and 3V from a 5V source, as shown in figure. Which combination of resistances, R1 , R2 and R3 gives the correct voltages?
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/477834/1/950928/Picture10.png)
A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of
, the reading of the spring balance will be-
A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of
, the reading of the spring balance will be-
A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading is-
A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading is-
A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up a plane of inclination with acceleration a0 is
A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up a plane of inclination with acceleration a0 is
In the situation shown in figure all the string are light and inextensible and pullies are light. There is no friction at any surface and all block are of cuboidal shape. A horizontal force of magnitude F is applied to right most free end of string in both cases of figure 1 and figure 2 as shown. At the instant shown, the tension in all strings are non zero. Let the magnitude of acceleration of large blocks (of mass M) in figure 1 and figure 2 are and
respectively. Then:
In the situation shown in figure all the string are light and inextensible and pullies are light. There is no friction at any surface and all block are of cuboidal shape. A horizontal force of magnitude F is applied to right most free end of string in both cases of figure 1 and figure 2 as shown. At the instant shown, the tension in all strings are non zero. Let the magnitude of acceleration of large blocks (of mass M) in figure 1 and figure 2 are and
respectively. Then:
A plank is held at an angle to the horizontal (Fig.) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. Acceleration and direction in which a man of mass m should move so that the plank does not move.
A plank is held at an angle to the horizontal (Fig.) on two fixed supports A and B. The plank can slide against the supports (without friction) because of its weight Mg. Acceleration and direction in which a man of mass m should move so that the plank does not move.