Question
In a circuit shown in figure, the potential difference across the capacitor of 2 F is
![](data:image/png;base64,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)
- 8 V
- 4 V
- 12
- 6 V
The correct answer is: 4 V
Related Questions to study
The effective capacitance between points
and
shown in figure. Assuming
F and that outer capacitors are all
F is
![](data:image/png;base64,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)
The effective capacitance between points
and
shown in figure. Assuming
F and that outer capacitors are all
F is
![](data:image/png;base64,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)
The four capacitors, each of 25
F are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is
![](data:image/png;base64,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)
The four capacitors, each of 25
F are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAACfCAYAAAAGcB6xAAAKdUlEQVR4nO3dT2gTeR8G8GdE3VKF9rLbqQiNLLg9xN2AoJ4khagRFeOecljYygpJlz300MUUBOupEQUrLLYVS+PJeBDrPxjXQIY96WHZQnPoLrxrqodO7SUFlaDQeQ8lWauZTKqZma/T5wO95DdpHu08+c2/TBTTNE0QkRgbvA5ARKuxlETCsJREwrCURMJs9DqAm8rlMh4/fgwACIVCaG9v9zgR0Yd8X0pd15HJZKBpGpaWlrBv3z4AwPT0NADg0KFDiMfjiMViXsYkqlL8ekpkdnYWyWQSiqLgxx9/RDQahaqqq5YplUrQNA03b95EsVjE8PAwotGoR4mJVviylNlsFufPn8elS5cQDocbes709DRSqRTC4TBSqZTDCYms+a6UIyMjePLkCSYnJ9HS0rLm56dSKRiGgUwm40A6Inu+Ovo6NTUFXddx48aNjyokAKTTaaiqinQ63eR0RI3xTSkNw0AqlVo9w81N4LCi4Ffd6lk6flUUHJ6YW/VoOp2GruvQNM2xvERWfFPKVCqFVCq1+jRH19cIAij8b67mc+YmzuMiBnD6p64PxtLpNAYHBx1KS2TNF6UsFovQdR29vb3vjexAdxTQZp9++KS5CSRPaYhe+wW1DgWFQiEEAgFMTU05EZnIki9Kmc1mEY/Ha4x04euVqRLvz5X6b6egWcySFcePH2cpyXW+KOXU1JTlyf8dK1MlVs2VcxM4fxEYyF+oOUtWxGIx3Llzp5lRiWz5opTFYhGBQKDmWNfKVIl3dyv1305Bi17DLzanMNvb2/HFF1/AMIzmhSWyYXuZ3dzcHM6ePWu50kuwsLDwwdU6VTu6EcVFzD4F0IV3ZsmfYL3h+p+2tjacOXMG27dvb2LitXv+/DkmJiY8zUDusJ0pf//9dxQKBTeyOOO9I7CNzpIVy8vL2LjR+0uE7969i2Kx6HUMcoNpY3Jy0uzt7bVbzFOBQMB8+vSpxWjRvBaFiYG8aRavmVHAHMg3/rs7OjrM+fn5puT8FPX/jeQnvtin7OrqqjOL/HcEdmKNs2RlX9Jy05jIAb4oZTweRzabtRxfOQJ7CqcuAgOnG9uXBABN0/ipEXKdL0oZi8Xw8OFDlMvlmuMrR2ABDORxocFZEqh3/pPIOb4opaqqiMViGBsbq71A+AJM04S5hkbquo5yucyZklzni1ICwOnTp3H9+vWmnFMsl8tIpVIYGRlpQjKitfFNKVVVxeTkJGKxmOVmbKNOnjyJ/v5+hEKhJqUjapxvSgmsXEQ+NDSEcDj8Uef0SqUSYrFY9b49RF7wVSkBIBqNYmxsDCdOnEA6nW541sxkMujp6UFvb2+NT5sQucd3pQRWZsx8Po+lpSWEQiEkk0lomrZqf7NUKkHXdfT39yMQCEDXddy+fZt3tSPPeX/9mEPa29sxPDyMRCIBTdNw+fJl/PXXX1hYWKiOf/fdd4jFYtB1XfS1vbS++LaUFYFAAMlkEslk0usoRA3x5eYr0eeMpSQShqUkEoalJBKGpSQShqUkEoalJBKGpSQShqUkEoalJBKGpSQShqUkEoalJBKGpSQShqUkEoalJBKGpSQSxvelLBQK6OzsRC6X8zoKCZfL5dDZ2en5t8yJLuXY2BhmZ2drjhmGgXQ67XIikmpwcNDyzoW6rmNqasrlRB9PdCmfPHmCx48f1xybnZ3Fw4cPXU5EUmWzWcu74+u6junpaZcTfTzRpfxYo6OjUBQFiqJg165dMAwDBw4cqD6WSCS8jkhCJBKJ6npx4MABGIaBXbt2VR8bHR11PZMvS9nX17fyhT6miZmZGaiqikePHlUfGx8f9zoiCTE+Pl5dLx49egRVVTEzM1N9rK+vz/VMrpYyl8tV34EqPzwAQ7Saq6WMRCLVd6DKTyQScTMCfSYqR83ffQP3YlPSC76/GXMwGMT8/LzXMWiNvPi7RSIREeuKL/cpiT5nLCWRMCwlkTAN7VMuLi5C13Wns6zS0tJiu8zLly8dz9Xa2oo9e/Y4+hqS/fHHH1heXvY6hq23b9/aLuP2OlzLmzdvcPDgwbrL2JZyaWkJf/75J86dO9e0YI3q6OiwHHvz5g3+/fdfx3MVCgU8ePBgXRbzwYMH6O3tRTAY9DqKrVKpVHfcMAxP1uH3PXv2DN9//z0uXLhguYxtKdva2hCNRjE5OdnUcI04efKk5djmzZvx7bffIp/PO5qhp6cHr1+/dvQ1pNqyZQuCwaDj/8fNsGPHjrrjqqpibGzMpTTWhoaGbJfhPiWRMCwlkTAsJZEwLCWRMCwlkTAsJZEwLCWRMCwlkTAsJZEwoj9POTw8jPb29ppj4XAYgUDA5UQkVT6ft1wf+vv7XU7zaUSXUlXVuuMsJVXUWxes3til4uYrkTAsJZEwLCWRMCwlkTAsJZEwLCWRMCwlkTAsJZEwoi8ekKBYLKKnp8frGADs70PjBF6g4T7OlDYCgQDy+fwH34GyHn7qXbpGzmEpiYRhKYmEYSmJhGEpiYRhKYmEYSmJhGEpiYRhKYkAjI6O4ptvvsGLFy+8jsJSkj9MT09bjpVKJRSLRRfTfBrRpTQMA+Vy2XLc7j/61atXOHbsGBKJRLOjkTAnTpywXB9GRkaQyWRcTvTxRJdycHAQ2Wy25piu63W/v5KonsobtqIoUBQFP//8M/755x90dHRUH8vlcp5kE11KIqds2bIF9+7dq17ne+XKFezcuRMLCwvVxyKRiCfZXC1lLpervgs59W5UKBTQ2dkJRVGwdetW3L9/H1evXq2+npSdebL27t+w8jM6Oup1LNe4+tGtSCQC0zQdfY1gMIj5+XkAK5so8Xgc27Ztw/j4uKOvS83z7t9wPeLmKxGAvr4+/P333/jqq6+8jsJSEknj6zsPVHbmiT4nnCmJhGEpiYSx3XxdWlqCpmme3Dyqo6Oj7vjy8jIOHz5c96qfT1UoFNDa2urY75fs1atXKBQKYm4cVs/i4mLdccMwRPw7isUiDh06VHcZ21K2tbVh9+7dGBgYaFqwRrS0tNiextiwYQOGh4dRKpUcy9Ha2oo9e/Y49vslO3LkCG7duoXl5WWvo9j64Ycf6o6rqop4PO5SGmuZTMb2Kx4bOtDz5ZdfIhwONyXUWjRybjEUCrmQZP3av3+/1xEasmnTJttlvFiH36fruu0y3KckEoalJBKGpSQShqUkEoalJBKGpSQShqUkEoalJBLG158SofUjkUhYXikj4aKBtRBdyr1792Lfvn01x7q7u22vIaT1I5VKWY6xlE2UTCYtx1RVrfuHIPpccZ+SSBiWkkgYlpJIGJaSSBiWkkgYlpJIGJaSSBiWkkgYlpJIGJaSSBiWkkgYlpJIGJaSSBiWkkgYlpJIGJaSSBiWkkgYlpJIGJaSSBiWkkgYlpJIGJaSSBiWkkgYlpJIGJaSSBiWkkgYlpJIGJaSSBjbL/h5+/YtZmZmMDQ05EYeIl/Tdd3ym+QqbGfKgwcPIhgMNi0U0XrW3d2No0eP1l1GMU3TdCkPETWA+5REwrCURMKwlETCsJREwrCURMKwlETCsJREwrCURMKwlETCsJREwrCURMKwlETC/B/Z9TztYQZZSQAAAABJRU5ErkJggg==)
For the circuit shown in figure the charge on 4
F capacitor is
![](data:image/png;base64,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)
For the circuit shown in figure the charge on 4
F capacitor is
![](data:image/png;base64,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)
A particle originally at a rest at the highest point of a smooth circle in a vertical plane, is gently pushed and starts sliding along the circle. It will leave the circle at a vertical distance
below the highest point such that
![](data:image/png;base64,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)
A particle originally at a rest at the highest point of a smooth circle in a vertical plane, is gently pushed and starts sliding along the circle. It will leave the circle at a vertical distance
below the highest point such that
![](data:image/png;base64,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)
Polar of origin (0, 0) w.r.t. the circle
touches the circle
, if
Polar of origin (0, 0) w.r.t. the circle
touches the circle
, if
Electrons ejected from the surface of a metal, when light of certain frequency is incident on it, are stopped fully by a retarding potential of 3 volts Photo electric effect in this metallic surface begins at a frequency 6 x 1014s -1 The frequency of the incident light in s-1 is [h=6 x 10-34J-sec;charge on the electron=1.6x10-19C]
Electrons ejected from the surface of a metal, when light of certain frequency is incident on it, are stopped fully by a retarding potential of 3 volts Photo electric effect in this metallic surface begins at a frequency 6 x 1014s -1 The frequency of the incident light in s-1 is [h=6 x 10-34J-sec;charge on the electron=1.6x10-19C]
Trajectories of two projectiles are shown in figure. Let
and
be the time periods and
and
their speeds of projection. Then
![](data:image/png;base64,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)
Trajectories of two projectiles are shown in figure. Let
and
be the time periods and
and
their speeds of projection. Then
![](data:image/png;base64,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)
A body is projected up a smooth inclined plane with a velocity
from the point
as shown in figure. The angle of inclination is
and top
of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of
? Length of the inclined plane is
, and ![g equals 10 m s to the power of negative 2 end exponent](data:image/png;base64,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)
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A body is projected up a smooth inclined plane with a velocity
from the point
as shown in figure. The angle of inclination is
and top
of the plane is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of
? Length of the inclined plane is
, and ![g equals 10 m s to the power of negative 2 end exponent](data:image/png;base64,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)
![](data:image/png;base64,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)
The equation of the circumcircle of the triangle formed by the lines
and y=0 is
The equation of the circumcircle of the triangle formed by the lines
and y=0 is
Which of the substance
or
has the highest specific heat? The temperature
time graph is shown
![](data:image/png;base64,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)
Which of the substance
or
has the highest specific heat? The temperature
time graph is shown
![](data:image/png;base64,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)
The figure shows a system of two concentric spheres of radii
and
and kept at temperatures
and
respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to
![](data:image/png;base64,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)
The figure shows a system of two concentric spheres of radii
and
and kept at temperatures
and
respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to
![](data:image/png;base64,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)
If the line y = x + 3 meets the circle
at A and B, then equation of the circle on AB as diameter is
If the line y = x + 3 meets the circle
at A and B, then equation of the circle on AB as diameter is
An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall
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)
An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall
![](data:image/png;base64,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)
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
Pole and polar are one of the important parts of the circle, many questions can be based on these parts. It should be remembered that while writing the equation of polar for a pole, the coefficients of square terms in the equation of the circle is one. If the equation of the circle does not have coefficients as one, then make it one before solving the question.
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
Pole and polar are one of the important parts of the circle, many questions can be based on these parts. It should be remembered that while writing the equation of polar for a pole, the coefficients of square terms in the equation of the circle is one. If the equation of the circle does not have coefficients as one, then make it one before solving the question.